1. EJERCICIO 11. Una deuda se expresa en sentido EJERCICIO 3negativo. Luego inicalmente el estadoeconmico de Pedro es - 60 bs.Al recibir 320 bs. Aumenta su capital1. + 32 m ; 16 mtantos bs. como ha recibido; entonces2. + 10 m ; 4 mla operacin queda expresada comose indica3. 50 85 = 35 m 60 + 320 = + 260 bs.4. 6 11= 66m2. 1.170 1. 515 = 345 sucres 5. -8 6 =-48 m3. 200 + 56 189 = + $ 67 9 6 =+ 54 m4. 665 1.178 + 2 . 280 = + 437 soles5. 20 15 + 40 75 = $ 306. 400 2 = + 800 m corredor 400 3 = 1. 200 m yo6. 67 + 72 16 + 2 = $ 9 7. Los 40 pies de longitud del poste7. 200 78 81 93 + 41 59 = 70 colones se reparten asi: 15 pies que sobresalen8. 45 66 79 + 200 10 = 0 - se asumen en sentido positivo- . 25 pies que se encuentran enterrados. - se asumen en sentido negativo - . Al introducir 3 pies ms, se adicionanEJERCICIO 2 a los que estan bajo el suelo y se deben descontar de los que estan por encima.1. 12 15 = 3Aritmticamente significa:2. 3 + 8 6 = 1 40 = 15 + 25 25 3 = 28 pies3. 15 ( 3) = 15 + 3 = 18 + 15 3 = + 12 pies ( )4. 8 + 5 = 8 + 5 = 135. 4 + 7 + 2 11= 68. 55 52 = + 3 m 9. 32 + 15 = 17m6. 8 + 4 1 = 8 + 4 = 4 7 am 10. 35 47 = 12 m 8 + 4 2 = 8 + 8 = 0 8 am 8 + 4 5 = 8 + 20 = + 12 11am 11. 39 + 56 = + 17m 12. 90 58 36 = 4 m7. 1 2 2 = 1 4 = 5 10 am 13. 72 30 1= 72 30 = + 42 m 1 2 3 = 1 6 = 7 11am 72 30 2 = 72 60 = + 12 m 1 2 3 + 3 1= 1 6 + 3 = 4 12 am 72 30 3 = 72 90 = 18 m 1 2 3 + 3 3 = 1 6 + 9 = + 2 2 pm 72 30 4 = 72 120 = 48 m8. 56 + 7 = 49 14. 120 ( 60) 1 = 120 + 60 = 60 Km9. 71 + 5 = 66 long 120 ( 60) 2 = 120 + 120 = 0 15 + ( 5) = 20 lat. 120 ( 60) 3 = 120 + 180 = + 60 Km 120 ( 60) 4 = 120 + 240 = + 120 Km10. 18 + 3 =+ 21 long65 -4 =+ 61 lat.11. -75 +135 =+ 60 aos

2. EJERCICIO 7. 27. 11a + 8a + 9a + 11a = 39a1. x + 2x = 3x 28. mx + 1 + 3mx + 1 + 4mx + 1 + 6mx + 1 = 14mx + 12. 8a + 9a = 17a 29. x2 y 8x2 y 9x2 y 20x2 y = 38x 2 y3. 11b + 9b = 20b 30. 3am 5am 6am 9am = 23am4. b 5b = 6b1 114 + 2 +1 + 8155. 8m m = 9m 31.a+ a+ a+a =a=a2 48886. 9m 7m = 16m 2 11 18 + 10 + 2 + 121 32. ax + ax +ax +ax =ax =ax7. 4a x + 5a x = 9a x5 2 1020 20 208. 6a x + 1 + 8a x + 1 = 14a x + 1 33. 0,5m + 0,6m + 0,7m + 0,8m = 2,6m9. mx + 1 5mx + 1 = 6mx + 111 1 34. ab ab ab ab 7 142810. 3a x 2 a x 2 = 4a x 2 4 2 1 2835 5 = ab = ab = ab1 1 1+ 1228 28 411. a+ a=a = a =a2 222 2 3 111 33 16ab + ab 735. x y x 3y x3y x y 3 69 1212. ab +ab = =ab51010102 4 6 4 3 337 3 = x y=x y 36361 1 2 +1 3113. xy + xy =xy = xy = xy3 66 6236. ab 2 + ab 2 + 7ab 2 + 9ab 2 + 21ab 2 = 39ab 21 4 1 4537. m m 8m 7m 3m = 20m14. xy xy == xy = xy5 555 38. x a + 1 8x a + 1 4x a + 1 5x a + 1 x a + 1 = 19x a + 15 21 20 3 2 23 215. a b a 2b = a b =ab1 1 11 1682424 39. a+ a+ a+ a+ a 2 3 45 67871530 + 20 + 15 + 12 + 10872916. a 8 a = 8 a = 8 a=a=a=a60 602017. 8a + 9a + 6a = 23a 111 1118. 15x + 20x + x = 36x40. ab ab ab ab ab 3 62 12919. 7m 8m 9m = 24m 12 6 18 3 443 =ab = ab36 3620. a 2b a 2b 3a 2b = 5a 2b21. a x + 3 a x + 8a x = 12a x22. 5a x + 1 3a x + 1 5a x + 1 = 13a x + 1 EJERCICIO 8 1 26+3+41323. a + a + a = a=a 1. 8a 6a = 2a 2 36 62 1 6 4 111 2. 6a 8a = 2a24. x x x=x= x3 6 6 63. 9ab 15ab = 6ab1 3 2 + 3 + 1015 3 4. 15ab 9ab = 6ab25. ax +ax + ax =ax =ax = ax51010 10 2 5. 2a 2a = 0359 10 12 231 2 6. 7b + 7b = 026. a x a x a x = a x= 2 2 2 a x46 12 12 7. 14xy + 32xy = 18xy 3. 8. 25x 2 y + 32x 2 y = 7x 2 y5 m + 1 7 m + 1 10 7 m +1 3 m + 1 1 m + 1 35. a a =a =a = a 6 12 12 1249. 40x 3 y 51x 3 y = 11x 3y1 2 12 1 2 11 2 36. 4a a = a = a 210. m2n + 6m2n = 5m2n33 311. 15xy + 40xy = 25xy3 20 + 317 37. 5mn +mn =mn = mn12. 55a 3b 2 81a 3b 2 = 26a 3b 24 4 413. x 2 y + x 2 y = 038. 8a x + 2b x + 3 25a x + 2b x + 3 = 17a x + 2b x + 314. 9ab 2 + 9ab2 = 07 m n m n 7+8 m n 1 m n 39. a b +a b = a b = a b 88815. 7x 2 y 7x2 y = 0 40. 0,85mxy 0,5mxy = 0,35mxy16. 101mn + 118mn = 17mn17. 502ab 405ab = 97ab18. 1024 x + 1018x = 6x EJERCICIO 919. 15ab + 15ab = 01 3 231 1. 9a 3a + 5a = 11a20. a a= a= a2 44 4 2. 8x + 9x x = 03 1 32 13. 12mn 23mn 5mn = 16mn21. a a= a= a4 2444. x + 19x 18x = 05 2 5 2 10 5 25 25. 19m 10m + 6m = 15m22. a ba b=a b=a b61212126. 11ab 15ab + 26ab = 0 4 2 9 28+ 9 21 2 7. 5a X + 9a X 35a X = 31a X23. x y +x y=x y=x y 714 14 14 8. 24a X + 2 15a X + 2 + 39a X + 2 = 03 5 3 10 724. am am =am = am 2 1 2 + 1 3 08 4 88 y+ yy=y= y=0 9. 3 33 335+3 225. am +am =am = am3 11 12 + 5 10175 5 5 10. m+ m m = m =m 5 42 20205 7 20 21 126. mn mn = mn = mn3 213+2 8 2 36 8 24 24 a b + a 2b a 2b = a b = a 2b 11.8488 3 2 11+ 3 2 827. a b + a b=a b = a 2b 2 12. a + 8a + 9a 15a = a 11 11 11 13. 7ab 11ab + 20ab 31ab = 15ab28. 3,4a 4b3 5,6a 4b 3 = 2,2a 4b 3 14. 25x 2 50x 2 + 11x 2 + 14x 2 = 029. 12yz + 3,4yz = 2,2yz , 15. xy 8xy 19xy + 40xy = 12xy30. 4a x 2a x = 2a x 16. 7ab + 21ab ab 80ab = 53ab31. 8a x + 1 + 8a x + 1 = 0 17. 25xy 2 + 11xy 2 + 60xy 2 82xy 2 = 36xy 232. 25ma 1 32ma 1 = 7ma 1 18. 72ax + 87ax 101ax + 243ax = 157ax33. x a + 1 + x a + 1 = 019. 82bx 71bx 53bx + 206bx = 01 m 2 1 m 2 1+ 2 m 2 1 m 2 20. 105a 3 464a 3 + 58a 3 + 301a 3 = 034. a+ a =a = a4 24 4 4. 1 111x x+ x x=30 20 + 15 12x= 13xEJERCICIO 1021.2 34560601 1114 4 + 2 1 122. y y+ yy=y=y 1. 7a + 6a 9b 4b3 36 12 12 127a + 6a = 13a 9b 4b = 13b3 21 2 1 2 = 13a 13b23. 5 a b 6 a b + 3 a b a b 218 5 + 10 30 2 7 22. a + b c b c + 2c a= a b=a b aa =0b b =0 c c + 2c = 0 30 30 =05 2 1 23 224. 6 ab 6 ab + ab 8 ab23. 5x 11y 9 + 20x 1 y 20 4 + 24 9 29 3 5x + 20x = 25x 11y y = 12y 9 1 = 10=ab = ab 2 = ab2= 25x 12y 10 24 24 825. a + 8a 11a + 15a 75a = 64a4. 6m + 8n + 5 m n 6m 1126. 7c + 21c + 14c 30c + 82c = 80c 6m m 6m = 13m 8n n = 7n5 11= 6 = 13m + 7n 627. mn + 14mn 31mn mn + 20mn = mn28. a 2 y 7a 2 y 93a 2 y + 51a 2 y + 48a 2 y = 05. a + b + 2b 2c + 3a + 2c 3b a + 3a = 2a b + 2b 3b = 0 2c + 2c = 029. a + a a + a 3a + 6a = 3a = 2a1 2 71x+ x x+ xx30.2 3 626. 81x + 19y 30z + 6y + 80x + x 25y3+47+3631 81x + 80x + x = 0 19y + 6y 25y = 0 30z= x= x= x662= 30z3 1 5 7. 15a 2 6ab 8a 2 + 20 5ab 31+ a 2 ab31. 2x + 4 x + 4 x + x 6 x 15a 2 8a 2 + a 2 = 8a 2 48 + 18 + 6 + 24 20 20 5=x=x= x 6ab 5ab ab = 12ab 20 31= 11 2424 6 = 8a 12ab 11 232. 7a x 30 a x 41a x 9a x + 73a x = 08. 3a + 4b 6a + 81b 114b + 31a a b33. a x + 1 + 7a x + 1 11a x + 1 20a x + 1 + 26a x + 1 = a x + 1 3a 6a + 31a a = 21a34. a + 6a 20a + 150a 80a + 31a = 88a4b + 81b 114b b = 30b35. 9b 11b 17b 81b b + 110b = 9b = 21a 30b36. a 2b + 15 a 2b + a 2 b 85 a 2b 131a 2b + 39 a 2b = 162 a 2b9. 71a b 84a b + 50a b + 84a b 45a b + 18a b 34 2 34 23 337. 84m2 x 501m2 x 604m2 x 715m2 x + 231m2 x + 165m2 x 71a 3b + 50a 3b 45a 3b + 18a 3b = 48a 3b= 1340m2 x 84a 4b 2 + 84a 4b2 = 05 3 2 2 3 2 1 3 2 5 3 2= 48a 3b38. a b + a b a b a b + 4a 3b 2634820 + 16 6 15 + 96 3 2 111 3 2 10. a + b c + 8 + 2a + 2b 19 2c 3a 3 3b + 3c=ab = ab 2424 a + 2a 3a = 2a b + 2b 3b = 0=37 3 2 a b = 4 5 a 3b 2 c 2c + 3c = 0 8 19 3 = 1488 = 2a 1439. 40a 81a + 130a + 41a 83a 91a + 16a = 28a40. 21ab + 52ab 60ab + 84ab 31ab ab 23ab = 0 5. 11. m + 71mn 14m 65mn + m m 115m + 6m 2 23223m + 6m = 7m33 3 m 14m m 115m2 = 129m2 22 271 65mn = 6mnmn= 7m3 129m2 + 6mn12. x y x y + x y 8x y x y 10 + x y 7x y 9 + 21x y y + 5043 2242 3 2 3 2 43x 4 y 8x 4 y + 21x 4 y = 14x 4 y x 3 y 2 + x 3 y 2 7x 3 y 2 = 7x 3y 2 x 2y x2y = 0 y3 10 9 + 50 = 31 = 14x y 7x y y + 31 4 3 2 313. 5a x + 1 3b x + 2 8c x + 3 5a x + 1 50 + 4b x + 2 65 b x + 2 + 90 + c x + 3 + 7c x + 3 8c x + 3 + c x + 3 + 7c x + 3 = 0 3b x + 2 + 4b x + 2 b x + 2 = 05a x + 1 5a x + 1 = 0 50 65 + 90 = 25= 2514. am + 2 xm + 3 5 + 8 3am + 2 + 5xm + 3 6 + am + 2 5xm + 3 x m + 3 + 5 x m + 3 5x m + 3 = x m + 3am + 2 3am + 2 + am + 2 = am + 25+86= 3m+3 m+2=xa 315. 0,3a + 0,4b + 0,5c 0,6a 0,7b 0,9c + 3a 3b 3c0,3a 0,6a + 3a = 2,7a 0,4b 0,7b 3b = 3,3b0,5c 0,9c 3c = 3,4c= 2,7a 3,3b 3,4c1 1 31 3 116. a + b + 2a 3b a b + 2 3 46 4 2132+837 1 12 18 1 17 3 1 32 1a + 2a a =a= a b 3b b =b=b = =24 4 4 3 66 6 4 24 47171= ab+4 643 2 1117. m 2mn + m2 mn + 2mn 2m251033 21 6 + 1 20 2 13 1 6 1+ 6 1m + m2 2m2 =m = m2 2mn mn + 2mn =mn = mn5 1010 10 333 13 2 1= m mn 10 318. 3 a 2 + 1 ab 5 b 2 + 2 1 a 2 3 ab + 1 b 2 1 b 2 2ab 34 26 46 33 2 7 2 9 + 28 2 19 2 1 3 238 9 a + a =a = aab ab 2ab = ab = ab4 31212 2 4 4 45 2 1 2 1 2 5 + 1 2 2 6 2 b + b b =b = b =b 26636 619 2 9=a ab b 2124 6. 3 2 2119. 0,4x y + 31+ xy 0,6y 3 x 2 y 0,2xy 2 + y 3 62 8 54222 2 3 23 16 2 14 2 ,,0,4x 2 y x 2 y = x y=0 xy 0,2xy 2 =xy = xy = 0,175xy 255 88 8 1 2,4 + 1 3, 14 3 0,6y 3 + y 3 =y = y = 0,35y 3 31 6 = 254 4 4= 0,175xy 2 0,35y 3 + 25 37 m 2 3 m1 1 m 2 1 a m1 b + a b 0,2a m 1 + b m 220. 2550 5 25 5 3 m 1 3 m 1 3 + 15 5 m 1 13 m 17 m 2 1 m 2 1 m 2 7 2 + 10 m 2 1 m 2 a + a 0,2a m 1 =a =ab b+ b =b =b255 25 2550 25 5 505013 m 1 1 m 2=a + b2550EJERCICIO 11Para resolver los problemas del 1 al 18 las literales toman los siguientes valores:a = 1 b = 2 c = 3 m = 1/2 n = 1/3 p = 1/41. 3ab = 3 1 2 = 64a4 1 4 22. 5a 2b3 c = 5 12 23 3 = 5 8 3 = 12012.= ==3bc 3 2 3 18 9 2 1 1 4 23. b mn = 2 = =2 2 2 3 6 3 11 5 2 2 20 5b m 2 2 24 = 5 = 6013.= = 2 3 1 111 1 614. 24m n p = 24 = 6 == 1 1 1 1 2 3np 2 34 27 4 108 18 3 41212 3 2 4 2 3 2 4 2 1 2 1 8 13 3 3 3 3 8 245. a b m = 1 2 = 4 = = 2 33 2 3 8 24 314. 4 b6 =4= 4 = 4 = =1 2 2 2 2 2 9 18 67 3 2 7 2 1 1 189 1 1 189 63c36.c p m = 33 = = =333 3 1212 4 2 12 16 2 384 1281 2 2 3 1 11 1 1 1 17. m n p = = =2m 2 = 1 = 1=3b c a 2 34 4 27 4 432 15.=n2 12 1 1 5 b 1 c 2 5 2 1 1 3 2 5 1 5 39 38. a m = 1 = = 66 26 2 12 1 1 249.2bc 2 = 2 2 32 = 4 9 = 36 = 624mn24 416. =2 3= 6=2 n2 p2 2 1 1 21 1 11 3 2 2210. 4m 12bc = 4 12 2 32 = 2 3 216 = 2 6 = 12322 3 4 9 161444 4 1 118 4== = 2411. mn 8a b = 8 14 23 = 64 = = 4 31 1 2 366 32 12 6 7. 3 3 64 2 3 3617. 3 64b c = 33 6= 3 3 64 8 729 = 3 3 373.248 = 3 72 = 216 2m1 2 233 1 3 4 33 318. apb 2 1 2 2 15 = 5 4= 5 4 = 5 =5 = 5 = 6 = 2 3 3250 3 3 125 3 515 75 25 125bm 3 3 125 2 1 3 3 222 2 2 2 22EJERCICIO 12Para resolver los problemas del 1 al 18 las literales toman los siguientes valores:a = 3 b = 4 c = 1/3 d = 1/2 m = 6 n = 1/41. a 2 2ab + b 2 = 32 2 3 4 + 42 = 9 24 + 16 = 11 1 1 4 + 12 + 9 25 22 11 1 12. c + 2cd + d = + 2 + = + + ==2 2 33 2 29 3 4 3636a b 3 43. + =+ = 9 + 8 = 17c d 11 3 21 c m62 2 72 + 6644. +2= 3 + 2 = 24 + 2 == d n1 133 32 4a 2 b 2 m2 32 42 62 9 16 365. + = += + = 3 8 + 6 =132 6 3 2 6 3 2 6313 1 1 1 1 1 10 + 546.c b + 2d = 4 + 2 = 2 + 1= =525 3 2 2 5 55 1 134 ab ac bd 3 43 2 = 12 + 1 2 = 48 + 2 1 = 144 + 6 1 = 149 = 49 2 +=+ 37. n d m11 61 1 63 33 4 24 2 114 + 1+ 12 178. b + n + 6m = 4 ++ 66 = 2 + + 6 == =8 2 1 4222 111 1 1 1 11 2 16 + 1139. c 3a d 16b + n 8d = 3 3 16 4 + 8 = 3 16 + 2 = 1 8 + = ==6 2 2 1 2 324 2 3 2 42 22 ma63 21610.=4 = = 216 16 = 3.456 11 b d 2 16 8. 22 1 11 13 4 11. 3 c 2 + 4n = 3 + 4 = 3 + 4 = 1 + 1 = 2 + 1 = 3 = 1 24m 46 4 6 12 24 24 24 8 22 4d 2 16n 2 1 1 2 8 1 112.+ 1= 2 + 8 1 = + 1 = + 1= 1 1 = 02 2 2 4 4 162 2 a + b b + m 3 + 4 4 + 6 7 10 = = = 21 20 = 113.c d 1 1 1 1 3 2 3 2 ba mb43 641 2++ 5a =++ 5 3 = + + 15 = 4 + 4 + 15 = 2314. n d1 1 1 1 4 2 4 2 1 1 12 3 16 312c a 16n a 13 4 1 43 431 13 4 + 48 4715. + = + = +2= +2= == 1 232bm d 246 18 6 8 62424 24 2 3a 6m 3 3 669 363 616. 4b += 44 + = 16 + = 4 + = 4 + 1 1= 4 36363 6 3 6 1 114 + 23 + 817. b + 2d 3c + 8d 2 32 2 + 1 1+ 2 3 3 6 3 3 = == = =2 4 2424 2 4 44 29 13 2 + 32 a b 3 2 + d 2 2 22 3 4 2 1 2 14424 2118.+ a n =+ 3 = + 33 4 34 4 342 3 9 2 12 3 2 3 24 2 39 3 64 + 9 12 61 5 =+ = + = 8+ = = =783 4 23 4 2 8 288EJERCICIO 13Para los problemas 1 al 24 las literales toman los siguientes valores:a = 1 b = 2 c = 3 d = 4 m = 1/2 n = 2/3 p = 1/4 x = 01. (a + b) c d = (1 + 2) 3 4 = 3 3 4 = 9 4 = 5 ()( ) ()(2. a + b b a = 1 + 2 2 1 = 3 1 = 3) 1 2 4 1 9 2 7+8 ( )(2 )3. b m c n + 4a = 2 3 + 4 1 = 2 3 2 + 4= + 4= + 4= 2 3 2 32 2 3 7 7 = 15 1 2 =724.(2m + 3n)(4 p + b ) = 2 2 + 3 2 4 4 + 2 = (1+ 2)(1+ 4) = 3 5 = 15 21 3 1 21 ()( 2 )( 42 2 ) 3 15. 4m + 8 p a + b 6n d = 4 + 8 1 + 2 6 4 = 2 + 2 3 0 = 0 2 2()2 ( ) 9. 2 1 1 ( )()( )( ) (6. c b d c b a m p = 3 2 4 3 2 1 = 1 1 1 )( )( ) 2 1 1 4 = 4 4 1 2 3+ 4 7 168 7 1612 (2 )2(7. b c + d a m + n + 2 x = 2 3 + 4 1 2 )()+ + 2 0 = 4 7 2 3 6 = 28 =6 6 = 6= 26 5 6 () 1 ()8. 2mx + 6 b + c 4d = 2 0 + 6 2 + 3 4 4 = 6 4 + 9 4 16 = 6 13 64 = 78 64 = 142 22 2 2 22 ( ) 1 1 816 8m 16 p + a=2+ 4 1 = 4 + 4 = 4 + 2 = 2 + 2 = 2 + 6 = 8 = 2 29. 9n b 3 9 22 18 2 63 3 3 3 3 (10. x + m a + d c = 0 + b c a ) 2 (1 + 4 3 ) = 2 (1+ 64 3) = 2 62 = 31 1 2 3 1 11 1 111.(4 m + p a 2 + b2 = 2) 4 + 4 1 + 2 22 2 + 1 1 + 4= 43 5 3 27= 4 = = =52 2 ac1 32 4 9 4 9 5 5 59 ()(12. 2m + 3n + 4 p 8 p + 6n 4m 9n + 20 p)() 1 1 11 2 1 = 2 + 3 + 4 8 + 6 4 9 + 20 = ( 1 + 2 + 1)(2 + 4 2)(6 + 5) = 4 4 11 = 176 2 2 2 3 4 43 2 3 4 (13. c m + n d m + p + b n + p 2 2 2 )()()1 2 1 1 2 1 73 11 21 44 126 144 + 44 26 = 32 + 4 2 + + 2 2 + = 9 16 + 4 = 12 += == 2 12 = 2 1 22 3 2 4 3 4 64 12 212 1212 6 c2 + d 2 2 32 + 4 2 2 1 9 + 16 2 1 25 2 11 5 m= = 2 1 2 2 = 1 2 2 = 5 2 = 2 = 2 2114. ad 1 4 15. (4 p + 2b)(18n 24 p) + 2 (8m + 2)(40 p + a ) 1 1 1 1 = 4 + 2 2 18 24 + 2 8 + 2 40 + 1 = (1 + 4)(12 6) + 2 (4 + 2) (11) = 5 6 + 2 66 = 30 + 132 = 1622 434 2 4 225+ 2 5+ d 24 1 2+ 4 1 6a+5 + 2 1+ b m = 2 22 4 = 2 5 + 8 = 3 5 + 8 = 3 13 = 3 208 = 624 = 31216. =d b p2 4 2 1 2 2 1 2 1 2 1 2 1 2 2 4 161616 16 22 90 2 88 2 () 2( )17. a + b c + 8b m n = 1 + 2 3 + 8 2 = 3 25 = 3 5 = 15 = 22 12 31 22 326 6 6= = 14 4 = 14 26 63 2 a+c 1+ 3 6 6n 1 44 (c + d ) p = (3 + 4)31 2 4 + += + 7 = =18. 2 b 22 4 2 2 2 7 7 2 10. ( )( )19. 3 c b 32m 2 d a 16 p 2 n = 3 (3 2) 32 2 (4 1) 16 = 3 16 6 4 = 3 4 6 2 3 = 12 12 3 = 31 1 2 62 4 2 2 3 6abc 3mn cdnp20. + 2 8b 2(b a ) abc 1 2 2 1 3 6 1 2 33 4 =+ 2 3 3 4 = 36 + 1 2 = 6 + 1 1 = 18 + 12 8 = 22 = 11 2 8 2 2(2 1) 1 2 3 2 16 2 6 8 2 32424 12 a 2 + b2 12 + 2 25 + 216 2212 + 3 (a + b)(2a + 3b) = 2 + 3 (1 + 2)(2 1 + 3 2) = + 3 3 8 = + 72 =5 521.== 73 2 b a22 123 3 33 3 2 1 1 1 1 1 1 22. b + + + + + 2 a b b c n m 2 1 1 1 1 1 1 22 3 5 3 5 7 21 49 70 35 = 2 + + + + + = 4 + + + 2 = 4 + + = +2 = = = 17 21 1 2 2 3 2 1 2 6 2 4 2 4 4 4 2 3 2 (2m + 3n)(4 p + 2c) 4m 2n24 189 4 185 2 2 1 2 1 1 2 = 2 + 3 4 + 2 3 4 = (1 + 2)(1 + 6 ) 4 = 3 7 = 21 =23. 1 44 == 20 9 5 2 3 4 2 3 4 999 99 c322 b2 22 3 n =3 3 = 3 3 = 3 4 = 6 4 = 54 28 = 2624. 2ab m b m 111 3 7 9 7 9 63632 1 2 2 4222 2 2EJERCICIO 141. a + b + m ( 10. $ x + a m )18. x2 m22. m2 + b3 + x 4 ( 11. m a b c Km)() (19. $ 3a + 6b ; $ ax + bm) 12. $ (n 300)3. a + 1 ; a + 220. (a + b)( x + y )4. x 1 ; x 2 13. (365 x) das21. $ (8 x + 48)5. y + 2 ; y + 4 ; y + 622. bs. (a 8)(x + 4) 14. $ 8a ; $15a ; $ ma (6. $ a + x + m)c 15. 2a + 3b +757. m n 223.sucres x (8. bs. x 6)16. a b m2a (9. x m Km) 17. 23n m2 24. $m 11. 3.00025. n 1 colonesa +b 29. $ m 2x26. a 3 solesx 30. x + 2 x + hab.2m m27.14 a 2a 31. 1000 a + + sucres3 4 . x +1 km28. h aEJERCICIO 15 3 21. m, n m + n20. 4x 2 y ,x y 8( )2. m , n m + n = m n 3 4x 2 y + x 2 y = 32 + 3 2x y=29 2x y3. 3a , 4b 3a + 4b 8 884. 5b , 6a 6a + 5b 33 mn , mn( ) 21.5. 7 , 6 7 + 6 = 7 6 = 1 84 3336 36. 6 , 9 6 + 9 = 3 mn mn = mn = mn 84 887. 2x , 3y 2x + 3y 22. a , b , c a + b + c8. 5mn , m 5mn + ( m) = 5mn m 23. a , b , c a b + c9. 5a , 7a 5a + 7a = 12a 24. a , b , 2c a b + 2c ( )10. 8 x , 5x 8 x + 5x = 8 x 5x = 13x 25. 3m , 2n , 4p 3m 2n + 4p11. 11m , 8m 11m + 8m = 3m 26. a 2 , 7ab , 5b2 a 2 7ab 5b212. 9ab , 15ab 9ab 15ab = 6ab 27. x 2 , 3xy , 4y 2 x 2 3xy 4y 213. xy , 9xy 9xy xy = 10xy 28. x3 , x2 y , 6 x3 x 2y + 6 ( )14. mn , 11mn mn + 11mn = mn 11 mn = 10mn 29. 2a , b , 3a 2a + 3a b = 5a b 1 21 215. a , b a b 30. m , 8n , 4n m 8n + 4n = m 4n 2 32 3 31. 7a , 8a , b 7a + 8a b = a b333 316. b, c b+ c 1 2 3545 432. x, y, x 2 3 4121 23 4617. b, b b+ b= b=b1 3 2 x x+ y= 2 12 x+ y= x+ y333 33 2 4 383 431 111218. xy , xy xy xy = xy = xy322 2222 33. 5 m , m , 3 mn 3 2 32 3528 219. abc , abc m m mn =m mn = m mn 5 5 53535 3 3 2 5 abc abc = abc = abc34. 7a 2 , 5ab , 3b 2 , a2 5 5 5 7a 2 a 2 + 5ab + 3b 2 = 8a 2 + 5ab + 3b 2 12. 35. 7mn2 + 17mn2 5m 4m = 10mn2 9m EJERCICIO 1636. x 7x 8x y + 4x y + 5 = 6x 4x y + 5 3 3 2 2 3 21. 3a + 2b c37. 5x 2 x 2 + 9xy 6xy + 7y 2 = 4x2 + 3xy + 7y2 10.ab + bc + cd 2a + 3b + c 8ab 3bc 3cd38. 8a 2b a 2b + 5ab 2 11ab 2 7b 3 5a + 5b5ab + 2bc + 2cd= 9a b 6ab 7b 2 2 3 2ab2.7a 4b + 5c 7a + 4b 6c39. m 8m n + 7m n + 7mn n32 22 311. ax ay az= m m n + 7mn n32 23c 5 ax 7ay 6az3.m+np 4 ax + 9ay + 8az1 12 140. a a + b+ b6 mn+ p2 43 5 ay + az2 110 + 3 1130=a+b6= a +b64 15 41512. 5x 7y + 84.9x 3y + 5 4x y + 641. a a 3b + 4b 8c + 8c = b x y +4 3x + 8y + 9 5x + 4 y 9 2x+ 2342. m3 + 5m3 5m3 4m2n 4m2n 7mn23x= m3 8m2n 7mn213. am + 6mn 4s5.a+ b c am 5mn + 6s43. 9x x 11y 6y + 4z 6z = 8x 17y 2z 2a + 2b 2c3am 5mn 2s 3a b + 3c am 4mn44. 6a + 9a 5ab 7b 8b 1122222b= 15a 5ab 15b 11 2 214. 2a + 3b6.p+ q+ r 6b 4c45. x y + x y 5xy + 7 xy 4y 8 2 2 2 2 3 3 4 2p 6q + 3r a+ 8c= 2xy 3 4y 4 8p + 5q 8ra + 9b + 4c 11 4r46. 3a a + b b 4 + 6 2 215. 6m 3n6 11 2 5 1 4n + 5p=a+b+2= a b+22 22 27. 7x 4y + 6z m 5p 10x 20y 8z1 2 3 2 2 15 5 5m 7nx + x + xy xy + y 2 y 2 5x + 24y + 2z47.243 36 6 2x2 + 3 2 2 15 2 1 16. 2a + 3b= x +xy = x + xy4 3 43 + 5c 48. 2m + 3n 6 8a +648. 5ax 5ax 6a x + 1 + a x + 1 + 5a x + 1 + 8a x + 2 = 8a x + 23m 8n + 8+ 7c 93 2 2 2 11 5m + n 1010a + 3b + 12c 749. x + x xy xy + y 2 + 5y 24 3 33 4m 4n 83+ 4 2 31+ 15 2 7 216 2 17. 2x 3y=x xy + y = x xy +y 43 343 + 5z + 99. 5a 2b 3c 6x 43 2 111550. a b a 2b + a 2b + ab 2 + ab 2 ab 27a 3b + 5c 3y544 2263 1+ 4 2 3+35 3 21 8a + 5b 3c 8x + 5z= a b+ ab = a b + ab 2246 26 6a c 13. 18. 8a + 3b c 21. 5a x 3am 7an24.a+ b c +d5a b + c 8a + 5a 9a xm na b + c da b c 2a + 3b 2c + d 11a x + 5am + 16an7a b + 4c 3a 3b + 4c d 14a x + 7am19a+ 3c 3a+ 2ca +122. 6m 7m a+2 5ma + 325. 5ab 3bc + 4cd19. 7x + 2y 4 a +1 a+2 a+3+ 2bc + 2cd 3de+ 9y 6z + 54m 7mm 2ab + 4bc+ 3de y + 3z 6 5ma + 1 + 3ma + 2 + 12ma + 3 ab 3bc 6cd8 x 3y 5 5ma + 1 11ma + 2 + 6ma + 32ab15x + 7y 3z 1026. a bbc20. m n p23. 8x + y + z + u c+dm + 2n 5c 3x 4y 2z + 3ua 6m+ 3p + 4 cd4x + 5y + 3z 4u 5m + 2n 8 a+d 9x y + z + 2u ad m + 3n + 2p 9 y + 3z + 2u2aEJERCICIO 177. m2 + n212. a3 4a + 5 + 4n2 3mna 3 2a 2 +61. x + 4 x 2 x 2 5x 5m 5n 22 + a 7a + 42 2x 2 x 4m2 3mn 2a a 2 11a + 15 32. a + ab28. 3x + x 3 13. x2 + x 6 2ab + b 2 4x 2 + 5 x 7x 23 +5 a ab + b22 x + 4x 6 32x 3+ 8x 5 3x 1 8x + 9x 623. x 3+ 2x x2+4 9. x 2 3xy + y 214. a3 b3 x x + 2x + 43 2 x + 3xy 2y2 2 + 5a b 4ab2 2 x 2 + 3xy y 2a 3 7ab2 b34. a 4 3a 2 x + 3xy 2y2 22a 3 + 5a 2b 11ab 2 2b 3 + a3+ 4a a 4 + a 3 3a 2 + 4a10. a 2 3ab + b 2 15. x 3 + xy 2 + y 3+ a 5ab b 22 x 5x y3 2 y35. x 2 + 3x 2a + 8ab b 222x 3 4xy 2 5y 3 x3+6b24x 3 5x 2 y 3xy 2 5y 3 x 3 x 2 + 3x + 611. 7x 2 + 5x 6 7m2n + 4n36. x 2 4 x16.4 x + 8x 9 2+m3 + 6mn n32 7x + 6 x2 7x + 14 m + 7m n3 2 + 5n3 3x 25 4 x 2 + 6x 1+ 6mn2 + 8n3 4x 2 11x + 1 14. 24. 8a 2m + 6am2 m317. x4 x2 + x+ a 3 5am2 + m3 + x 3 4x 2 +5 4a + 4a m 3am232+ 7x 2 4x + 6+ 7a 2m 4am26x 4 + x 3 + 2x 2 3x + 11 3a + 3a m 6am322618. + a + a4+6625. x5 x 3y 2 xy 4 +a 5 3a3+8+ 2x y4+ 3x y2 3 y5+ a 3 a 2 14+ 3x y3 2 4xy y 54+ a + a + a 2a a 65432 x5 + 5xy 4 + 2y 52x 5 + 2 x 4 y + 2 x 3 y 2 + 3x 2 y 319. x5+ x 9 + 3x 4 7x 2+6 26.a 5 + a6 + a2 3x 3 4x + 5 + a 4 + a3 + 6x 5 + 3x 4 3x 3 7x 2 3x + 2 + 3a 2 8 + 5aa5 4a 2 + 6 5a20. a + a+a+a +a +4 36 4 3+ a2 + 527.a4 b4 + 4a + 7 a 2 a 3b + a 2b 2 ab 3 8 a2 6 3a + 5a 3b 4a 2b 24a 3 + 5a 1 4a 3b + 3a 2b 2 3b 4 2a 4 ab 3 4b 421. x4 x 2y2 5x 3 y + 6xy 3 28.m3 n3 + 6m2n 4 xy 3 + y 4+ n3 4m2n + 5mn2 4x y2 2 6m n33+ 6mn2x 4 5x 3 y 5x 2 y 2 + 2xy 3 + y 4 6 2m + n 2m n3 3 2 11mn222. + x + xy 229. ax 3a x 2 x 2 + 4 xy 7y 2 x 1 + 5a + 6a x 3 x 2 + 6xy + 5y 2+ 7a x 3 + a x 4 6x 2 4xy + y 2+ ax 1 13a x 3 7 x 2 + 7 xy y 2x 1x2a + 6a x 3a + ax 423.a 3 8ax 2 + x 330. a x + a x + 1 + ax + 2 6ax x + 5a x232 3a x+3ax 1 +a x23a 3 x 3 5a 2 xa x+ 4ax+3 5a x + 2a + 14ax x 323+a x 1 a x2+ ax + 25a 3 2x 3 2a x + a x + 1 + a x + 3 3a x + 2x+3 x+2 x +1a 3a+a 2a x 15. 5 2 2 23EJERCICIO 18 6.x y+ xy 6 34 1 211. x +xy 1 x2 + 1 2 y1xy 236 821 1+ xy + y21 x2 + 1 2 y+5xy2 43 46 1 2 2+3 1 1 51 5 1 2 2 16 + 3 + 6 2 9 6 + 10 x + xy + y 2 = x 2 + xy + y 2x +y + xy 2 6 4 2 64 6 241227 2 13 1137 2 1= x2 y +xy x 2 + xy y2. a + 2 ab2 6 24 12 312 24 11 21 2 7. a 3 ab +b3 ab +b2 42 3 25 2 11 ab 2b 3 + a b ab b286 45 1 33 31 2a b a b 2 1 152 2 3 2452 a +2ab + b = a2 +b4 10104 + 1 3 4 3 2 5 10 3 3 5 3 2 a + ab + b + a b 4 8 5 65 78251 78 2= a 3 ab 2 b 3 + a 2b a 3 + a 2b ab 2 b 33. x 2+xy 4 85643 85 3 1 8. x4 x2 + 5 xy + y2 62 3 33 +x x 52 3 8 xy + y2 63 3 45 33 x+ x x 4 1 53+2 2564 x2 + xy + y 63 53 4 24+5 3 36x x + 2+ x + x 251556 8 = x 2 xy + y 2 = x 2 xy + y 2 6333299 2 39= x 4 x2 + 2 + x3 x x4 + x 3 x 2 x + 2 568 5 28 3 21 2 2 3 12 34. x y9. m mn2 +n 42 3 452 1 2 13 31 2xy + y+mn2 n+ m n5 6 8561 2 11 2 m3 n3 m n+ xy +y 21032 + 3 3 2 + 1 2 2 3 5 3 1 3 2 3 2 4 +1 3 + 1+ 2 2 3 2 3m +mn +n +m n x +xy + y = x xy3 856 4 106410 5 16 251 16= m3 mn2 n3 m2n m3 m2n mn2 n 338 5 633 852 2 1 1 22 45.a+ab b10. x 4+ 2x 2 y 2 + y35275 2 1 1 2 5 4 3 2 2 1 4 1 3a ab + b x + x y y xy610 6 6 814 6 1 2 2 1 4 5 31 211 2 x y + y x y a+ab b4 7 6 12 2036 5 4 16 + 3 2 2 2 4 1+ 2 4 1 3 5 3 8 + 10 1 2 4 2 + 1 3 + 1 2 2 x +x y + y xy x y a +ab + b6 814 661220 61 17 2 2 5 4 1 3 5 3= x4 +x y +y xy x y 17 2 3 417 2 326814 6 6 =a +ab b2 =a +ab b2 12 20612 20 31 4 5 3 17 2 2 1 3 5 4 x x y+ x y xy + y66 8 6 14 16. 2 3 411. x + 13. a +6 5 x x a4 a2 3 5 3 5 3 31 1 3 2+a a a 3x 5 x + x 58 210 8 3 45 21 3 1 2 2 4 a a+6 +xx x786 4 3 31 33 a 6 x + x4 8 1257 3 4 85 2 3 5 3 3 43 8 + 2 1 3 8 1+ 632 2 2 4 a6 + a +a + a a + a 2x 5 +x + x+x x 47 8 58 8 12 108310 4 3 2 3 5 3 3 7 = a6 a + a + a a a 78 58 8 7 3 1312= 2x 5 x +x + x2 x4 4 3 5 10 4 3 3 3 2 712 1083 a6 + a a a + a a57 8 8 8 27 3 1 2 13 2x 5 x 4 x + x +x 4 3 12 8 102 3 5 21 3 14. x5 y512. a+ax x 1 3 2 3 4 1 59 63 + x y xy y10463 7 21 3 a2x ax x 1 5 y+3 45x y x2y37 89 9562 3 21 5 2 11 2 x y y+ 2x 4 y a3 + a2x ax53 3 24 1 4 3 2 3 4 18 3 2 6 5 3 + 10 45 x5 +x y xy +y + x y x2y3 26 3 6+7 220 21 6 2 3 1 3104 1856a + a x+ax + x 3 3 2 3 4 29 5 13 4 59 1424 9 = x5 x y xy y +x y x2 y 3104 185641 27 4= a3 + a xax 2 x 3 x5 +13 4x y3 3 2 5 2 3 3 4 29 5x y x y xy y9 142495 106418EJERCICIO 19Para los problemas 1 al 14 las literales toman los siguientes valores:a = 2 b = 3 c = 10 x = 5 y = 4 m = 2/3 n = 1/5 3. x4 y41. 4x 5y2x 4 5x 2 y 2 8 3x + 6y 8 4x4 + 7x 3y + 10xy 3 x+ y x 4 y 4 5x 2 y 2 8 + 7x 3 y + 10xy 3 2y 8 x 4 + 7x 3 y 5x 2 y 2 + 10xy 3 y 4 8 24 8 = 8 8 = 0= 54 + 7 5 3 4 5 52 4 2 + 10 5 4 3 4 4 8= 625 + 28 125 5 25 16 + 50 64 256 8= 625 + 3.500 2.000 + 3.200 256 8 = 3.8112.x 2 5x + 8 x 2 + 10x 30 4.3m 5n + 6 6x 2 + 5x 50 6m 20n + 8 6x 2 + 10x 7212m 20n 12 6 5 2 + 10 5 72 = 6 25 + 50 72 9m 45n + 2 = 150 + 50 72 = 172 2118 45 9 45 + 2 = + 2 = 6 9 + 2 = 1 35 3 5 17. 5.nx + cn ab 8nx 2cn ab 10.x 3 y xy 3 + 5nx ab 5 5x 3 y 6 + x 4 x 2y2 10nx cn 3ab 5 6xy + 23 + x2 y21 1 10 5 10 3 2 3 5+ 3xy 3 + 1 y45 56x 3y 4xy 3 + 2 + x 4 y4 50 10 = 6 3 5 x + 6x y 4xy y + 24 33 45 5 = 10 2 18 5 = 15 = 5 4 + 6 53 4 4 5 43 44 + 2= 625 + 24 125 20 64 256 + 26. a3 + b3= 625 + 3.000 1280 256 + 2 = 2.091 . 3a b + 8ab b 3 22 5a 3 6ab 2 +8 3 2a 2 2 b +11. + 3a b2 2b3 43 1 1 4a3 + 2ab 2b3 + 82 ab + b 2 3 9 4 2 + 223 23 + 83 23 1 1 + ab b 2 = 4 8 + 4 9 2 27 + 86 3 = 32 + 36 54 + 8 = 423 2 2 +16 + 1 3 2a ab +b4 697. 27m 3 + 125n 3 3 1 4= a 2 ab + b 2 9m n + 25mn 22 4 6 9 14mn 283 14 22 2 3 + 32 + 10m n + 11mn 2 2 4 6931 4 27m3 + m2 n + 22mn 2 + 125n 3 8= 4 6 + 9 = 3 1+ 4 = 6 322 346 9 2 2 1 2 1 1 27 + + 22 + 125 8 3 3 5 3 5 5 9 2 25 218 4 1 44 11m +n = 27 + + + 125 8 12. 17 34427 9 5 3 25 125 7 25 21 4 444 44m +n+ 15mn =8++ + 1 8=++134 17245 75 45 75 7 2 1 20 + 132 + 225 377 m 30mn == = 1 152225 34 4225 225 + 3 a 1+ y b 2 + mx 418 + 7 7 2 25 + 10 2 1 + 2 1 + 128. xm +n + 45mna 1 b2x 434344 2x 2y 2m 18 2 35 2 12 b2=m +n + 45mn + 3y 2m x 4 34 3449 235 2 3x a 1 + 2 y b 2 3mx 4 17m 45mn + 34n +354 2 22 9 2 2 1 35 1 3 52 1 + 2 4 3 2 3 = 15 + 8 2 = 21 = 45 +17 3 +33 5 34 5 39 4 90 35 1 = + +3b 1 x 317 9 15 34 259.n m+8 4 354 7= 6+ + 3=+ 3 5nb 1 3m x 3 + 10 17850 17 17040 + 7 5104634nb 1 + 5m x 3 18= = = 2 123 170 170170 mx 3 53 2 224 = = 3 39 18. 1 2313. b m cn 214. 0,2a 3 + 0,4ab2 0,5a 2b253 2 1+ 0,6ab2 0,3a 2b 0,8b 3b m cn +6410 0,4a 3 0,8a 2b +61 21 b m+ cn +40,2a 3 + 15a 2b + 0,9b3,4 251 b 2m +2cn + 3ab 2 0,1a 2b + 0,1b 3 + 685 0,1a b + ab + 0,1b3 + 6224 + 6 2 1 2 30 5 + 2 + 100 10 + 30 + 20 + 3b m+cn += 0,1 22 3 + 2 32 + 0,1 33 + 68 50 5 7 26743 7 2 2 67 1 43= 0,3 4 + 2 9 + 0,1 27 + 6 b m+ cn += 3 +10 + 850 5 8 3 50 55= 12 + 18 + 2,7 + 6 ,7 9 2 67 43 126 670 43 21 67 43= ++ = ++=+ + = 25,52450 524 250 5 4 25 5525 + 268 + 8601. 653= == 16 100 53 100100EJERCICIO 2021. 8x a + 2 11= 8xa + 2 111. 8 5 = 1322. 6a n ( 5a n ) = 6a n + 5a n = 11a n2. 7 4 = 113. 8 11 = 3 23. 45a x 1 ( 60a ) = 45a + 60a = 15ax 1x 1 x 1x 14. 8 ( 11) = 8 + 11 = 324. 54bn 1 ( 86b ) = 54b + 86b = 140bn 1 n 1n 1 n 1( )5. 1 9 = 1 + 9 = 86. 2a 3b = 2a 3b25. 35ma ( 60m ) = 35m + 60m = 25m aaaa7. 3b 2 = 3b 2 11 10 + 1 11 126. 5 = 5 + = 2= =528. 4x 6b = 4x 6b 2229. 5a 6b = 5a 6b2 3891727. == ( )10. 8 x 3 = 8 x + 3 3 4 12 1211. 9a 5b2 = 9a 2 5b 2 21 2 2 2 1 2 2 2 3 2 228. x x = x + x = x = x3 3 3 3 3( )12. 7 xy 5 yz = 7 xy + 5 yz4 3 5 3 24 + 25 3 49 313. 3a 4a = a 29. x y x y =x y=x y5 6 303014. 11 2 25 m2 = 14m2m1 2 3 2 1+ 6 2 5 2 6 x 2 y ( x 2 y) = 6x 2 y + x 2 y = 5x 2 y 30. ab ab = ab = ab15. 8 4 8 811a 3m2 ( 7a 3m2 ) = 11a 3m2 + 7a 3m2 = 18a 3m231. 2 3 = 516.( )32. 7 1 = 7 + 1 = 817. 8ab 2 ( 8ab 2 ) = 8ab 2 + 8ab 2 = 033. 8 ( 5) = 8 + 5 = 318. 31x 2 y ( 46 x 2 y) = 31x 2 y + 46 x 2 y = 77 x 2 y34. 5 ( 4 ) = 5 + 4 = 919. 84a 2b ( 84a 2b) = 84a 2b + 84a 2b = 0 35. 7 ( 7) = 7 + 7 = 020. 3a x + 1 5b x + 2 = 3a x + 1 5b x + 2 36. 2a ( 5) = 2a + 5 19. 37. 3x b = 3x bEJERCICIO 2138. 2n 5m = 2n 5m1.a +b2. 2x 3y (39. 3b 6a = 6a + 3b) a +bx 2y40. 8b ( 5a ) = 5a + 8b 332b3x 5y41. 7a ( 9 ) = 7a + 93. 8a + b 4. x 3x2 (42. 25ab 25 = 25 ab + 25 ) 3a 4 5x 6 11a + b 4 x 2 + 2x 6 ( )43. 3a a = 3a + a = 4a44. 4b ( 3b) = 4b + 3b = b 5. a a b326. xy+z54 x 3 ( 11x 3 ) = 54 x 3 + 11x 3 = 65x 3 7a 2b 9ab 2x+yz45. a 3 8a 2b 9ab 2046. 78a 2b 14a 2b = 64a 2b47. 54a 2 y ( 43a 2 y ) = 54a 2 y + 43a 2 y = 11a 2 y48. ab 9ab = 10ab 7. x + y z8. x 2 + y 2 3xy x+ y z 3x 2 + y 2 + 4xy49. 31x y ( 31x y) = 31x y + 31x y = 02 22 2 2 x + 2 y 2z 2x 2 + 2y 2 + xy50. 3a a = 4a x xx 2x 2 + xy + 2y 251. 311a x +1 ( 7a x +1 ) = 311a x +1 + 7a x +1 = 318a x +19. x3 x2 + 610. y2+ 6y 3852. 105m 9m = 96m x xx 5x 6 + 4 x 23y 2y 24 6y53. 31ax 1 18a x 1= 49a x 1 x 6x 2 3 + 4x4 y 2 2y 4 + 6y 3 6 y 8 2y 4 + 6 y 3 + 4 y 2 6y 854. 236ma ( 19m ) = 236maa + 19ma = 217ma55. 85a x + 2 54a x + 2 = 139a x + 211. a 3 6ab 2 + 9a + 8a 15a 2b 556. ( 6a ) = + 6a 1 1 4 4a 3 6ab 2 + 17a 15a 2b 5 2 2 + 15 13 a 3 15a 2b 6ab 2 + 17a 557. ( 5) = = 33312. x 4 + 9xy 3 11y 4 7 3 3 358. m m 20y 4 + 8x 3y + 6x 2 y 2108 56 30 3 86 343 3x 4 + 9xy 3 31y 4 + 8x 3 y + 6x 2 y 2=m =m =m 80 8040 x 4 + 8x 3y + 6x 2 y 2 + 9xy 3 31y 4 5 2 2 11 2 2 13. a + b + c d ab + 2ac 3cd 5de59.a b ab 14. 6 12 8ab + 4ac + 5cd 5dea + bc+d 10 + 11 2 2 21 2 2 7 2 2 = ab =ab = ab2a + 2b 7 ab + 6ac + 2cd 10de 12 12 415.x 3 + 6x 2 9x 191 3 260. a b 45a 3b 2 6x 3 + 11x 2 21x + 439 1 405 3 2 406 3 2 5 x 3 + 17 x 2 30x + 24= ab = a b = 45 9 a 3b2199 20. 16. y 9y + 6y 31 53 2 31y 3 + 8y 2 + 11y 4 + 19yy 5 40y 3 + 14 y 2 + 11y 4 + 19y 31 y 5 + 11y 4 40y 3 + 14 y 2 + 19y 3117.5m3 9n3 + 6m2n 8mn2 5m3 + 21m2n 14mn2 + 18 9n3 + 27m2n 22mn2 + 18 27m2n 22mn2 9n3 + 1818.4 x 3 y 19xy 3 + y 4 6x 2 y 225x 3 y + 51xy 3 32 x 2 y 2 + x 429x 3 y + 32 xy 3 + y 4 38x 2 y 2 + x 4 x 4 + 29 x 3 y 38x 2 y 2 + 32 xy 3 + y 419. m + m n 9m n + 19 6 4 2 2 4 + 30m2n4 + 61+ 13m3n3 16mn5m6 + m4n2 + 21 2n4 + 80 + 13m3n3 16mn5 m6 + m4n2 + 13m3n3 + 21m2n4 16mn5 + 80m20. a 5b + 6 a 3b 3 18 ab 5 + 428a 6+ 11a b 4 2 + 11a b2 4 9b 68a 6 a 5 b + 11a 4 b 2 + 6a 3b 3 + 11a 2b 4 18 ab 5 9b 6 + 4221. 1 x + x x + 3x 6x 2 4 3524 + 30x 2 8x 4 15x+ x625 + 29 x 2 7 x 4 x 3 12x 6x 5 + x 6 x 6 6 x 5 7 x 4 x 3 + 29 x 2 12 x + 2522. 6x 2 y 3 + 8 x 5 23x 4 y + 80x 3 y 2 18 + 51x 4 y + 21x 3 y 2 80 + y 5 9xy 4 6x 2 y 3 + 8 x 5 + 28x 4 y + 101x 3 y 2 98 + y 5 9xy 4 8x 5 + 28x 4 y + 101x 3 y 2 6 x 2 y 3 9xy 4 + y 5 9823. m6 8m4n2 + 21m2n4 6mn5+ 8 23m n5 14m n 3 3+ 24mn5 8n6 + 14m6 + 23m5n 8m4n2 14m3n3 + 21 2n4 + 18mn5 8n6 + 22m24. x 8x + 16x 23x 15 75 2 51x+ 18 + 8 x 6 25 x 4 + 30x 3x 7 59x + 16x 5 23x 2 + 3 + 8x 6 25x 4 + 30x 3 x 7 + 8x 6 + 16x 5 25 x 4 + 30x 3 23x 2 59 x + 325. 9a 6 15a 4b 2 + 31a 2b 4 b 6+ 14 + 15a b4 2 3 b 25a b 53 a b + 9 ab6 53 359a 6+ 31a b 4b 6 25a 5b 53 a 3b 3 + 9 ab 5 + 14 9a 6 25a 5b 53 a 3b 3 + 31a 2b 4 + 9 ab 5 4b 6 + 142 4 ax + ax +1 ax + 2 5a x + 6a x + 1 + a x + 226. 4a x + 7a x + 1 21. a 127. m m a + 3ma 24ma 5ma 2 3ma + 1 8ma 35ma ma 1 2ma 2 3ma + 1 8ma 3 3ma + 1 + 5ma ma 1 2ma 2 8ma 3m+428. a 7am + 2 8a m + 6am 1+ 14a m + 2+ 8a m 1 + 5am + 3 + 11a m + 1a m + 4 + 7a m + 2 8am + 14a m 1 + 5am + 3 + 11a m + 1 am + 4 + 5am + 3 + 7am + 2 + 11a m + 1 8a m + 14a m 1a+229. x 7 x a + 9x a 1 + 25x a 2 19x a 45x a 1+ 11x a + 1 60x a 3a+2 a 1 a2x 26x 36x a + 25x + 11x a + 1 60x a 3 x a + 2 + 11x a + 1 26x a 36x a 1 + 25x a 2 60x a 3 n+1n230. m 6m+ 8mn 3 19mn 5 5mn 2 6mn 3 9mn 5 8mn mn 4mn + 1 11mn 2 + 2mn 3 28mn 5 8mn mn 4 mn + 1 8mn 11mn 2 + 2mn 3 mn 4 28mn 5EJERCICIO 22b a 7. a + 2b 3cb a a + b 2c1. 2b 2a 2a + 2b 2a + 3b 5c2. 2x + 3y 8. 3n + 4m + 5p x+y + n m p x + 4y 2n + 3m + 4p 3m 2n + 4p3. 7a + 59. x + 3y 6z5abxy +z 2a + 5 b 2a b + 5 2x + 2y 5z4. x 2 + 6 10. 5b 2 + 8ab + a 2 x 2+ 5x 6b 2 ab 3a 2 2x + 6 + 5 x 2 x + 5 x + 622b 2 + 7ab 2a 2 2a 2 + 7ab + b 25. x 2 y + 5xy 2 5m2 n2 + 6mn+ xy 2 x 3 m2 + n2 + 3mn 11. x 2 y + 6xy 2 x 3 x 3 + x 2 y + 6 xy 2 6m2 + 9mn6.7a 2b + 5ab 212. 8x 2 + 5x 4 6a 2 b+ 8a 3+ x 6 + x3a b + 5ab + 8a 8a + a b + 5ab223 32 2 8x 2 + 6 x 10 + x 3 x 3 8x 2 + 6x 10 22. 14m2 8n + 1623. y + y + y + 96 3 213. 14m2 9 m 3 23y 3+ 5 8y 4 + 15y 5 + 8y 8n + 7 m3 m3 8n + 7 y 6 22y 3 + y 2 + 14 8y 4 + 15y 5 + 8y y 6 + 15y 5 8y 4 22y 3 + y 2 + 8y + 1414. 8ab + 5bc + 6cd ab + bc 6cd 24. x x + 3x 5x 98 6427 ab + 6bc 36 7x 7 5x 5 + 23x 3 51x15. a 9a b b 323 x 8 x 6 + 3x 4 5x 2 45 7x 7 5x 5 + 23x 3 51x 25a 2b + b 3 + 8ab 2 x 8 7x 7 x 6 5x 5 + 3x 4 + 23x 3 5x 2 51x 45a 3 34a 2b+ 8ab 2 25. x 7 3x 5 y 2 + 35x 4 y 3 8x 2 y 5 + 6016. 6x 8x y 6xy 322+ 60x 4 y 3 + x 2 y 5 y 7 90x 3 y 4 + 50xy 6 xy 2 + 6y 3 4 x 3x y + 95x y 7 x y + 60 y 7 90x 3 y 4 + 50xy 675 2 4 32 5 x 7 3x 5 y 2 + 95x 4 y 3 90x 3 y 4 7x 2 y 5 + 50xy 6 y 7 + 606x 3 8x 2 y 7xy 2 + 6y 3 4 x+317. m2 9n + 11c + 14 26. a 8a x + 1 5 m2 7n + 8c d + 5a x + 1 a x + 2 + 6a x 16n + 19c + 14 d 19c d 16n + 14a x + 3 3a x + 1 5 a x + 2 + 6a x a x + 3 a x + 2 3a x + 1 + 6a x 518. 5a + 9a b 40ab 3 + 6b 443 7a 3b + 8a 2b 2 5ab 3 b 4 27. 8an + 16an 4 + 15an 2 + an 35a 4 + 2a 3b + 8a 2b 2 45ab 3 + 5b 4 7an 5an 2 an 3 8an 1 15an + 16an 4 + 10an 2 8an 119. x 5 8x 4 + 25x 2 + 15 n 1 n2 15a 8a n + 10a + 16an 4 6x 2 + 7 6x 3 + 9xx 5 8x 4 + 19x 2 + 22 6x 3 + 9x 28. 15x a + + 5x a + 6x a + 41x a 32 1 x 5 8x 4 6x 3 + 19x 2 + 9x + 22 + 9x a + 2 + 18x a 1 31x a + 1 + x a + 420. 3xy 4 8x 3 y 2 19y 5 + 1815x a + 3 + 14x a + 2 6x a + 59x a 1 31x a + 1 + x a + 4 6xy 4 25y 5 x +x y 52 3 x a + 4 + 15x a + 3 + 14x a + 2 31x a + 1 6x a + 59x a 1 9xy 4 8x 3 y 2 44y 5 + 18 x 5 + x 2 y 3 x 5 8x 3 y 2 + x 2 y 3 9xy 4 44y 5 + 18 m 1 29. 9a 21am 2 + 26m 3 + 14am 5 5am 1 12am 2+ am + 8am 421.x 3 6x 4 + 8x 2 9 + 15x 25x 3+ 18x 2 + 46 25x + 11x 514am 1 33am 2 + 26m 3 + 14am 5 + am + 8am 4 am + 14am 1 33am 2 + 26m 3 + 8am 4 + 14am 5 24x 3 6x 4 + 26x 2 + 37 10x + 11x 5 11x 5 6x 4 24x 3 + 26x 2 10x + 37 30. 15mx + 3+ 50mx + 1 14mx 6m x 1 + 8mx 222. a5 26a 3b 2+ 8ab 4 b 5 + 6mx+4+ 23m x+2+ 6mx + 1 + mx 1 8a 4b a 3b 2 + 15a 2b 3 + 45ab 4 +8 m x+4 15m x+3+ 23m x+2+ 56m x +1 14m 5mx 1 + 8m x 2xa 8a b 27a b + 15a b + 53ab b + 14 5 43 2 2 345 23. EJERCICIO 23 11. x 12 xy y 21. 1 a +1x 2 1 xy y 2 x 2 xy y 2 1 a+2 12. a 3+62. 0 5a 2b + 8ab 2 b 3 a+8 a 3 5a 2b + 8ab 2 b 3 + 6 a+8 13. x 3 + y3 9+ 5 x y 17 xy22+53. 3a a + 5 2 x + 5 x y 17 xy + y + 5 322 3 3a a 4 a 3a 4 22 14. x 414. + 16 9 x y + 8x y + 15 xy32 23 5xy + x 162 x 9x 3 y + 8 x 2 y 2 + 15 xy 3 1 4 5xy + x 2 x 2 5xy 15. a 5+ b5 + 11a b 2a b 8a b + 4ab42 33 2 45. 1 a + 11a 4b 2a 2b3 8a 3b 2 + 4ab 4 + b5 5 a 3 + a 2b ab 2 a 5 + 11a 4b 8a 3b2 2a 2b3 + 4ab 4 + b5 1 a + a b ab a + a b ab + 13223 2 2 16. x 4+ x2 + 506. x 3 5x 3 + 25xx 3 + 8 x 2 y + 6xy 2 x 4 5x 3 + x 2 + 25x + 50 2x 3 + 8x 2 y + 6 xy 2 17. y + y 416 37. a 9y 5 17y 4 + y 3 18y 2 + 8a 2b 6ab 2 + b 3 y 6 + y 41 9y 5 17y 4 + y 3 18y 2 a 3 + 8a 2b 6ab 2 + b 3 y 6 9y 5 17y 4 + y 3 18y 2 + y 418.+ y4 18. a 6+ 9a 4b 2 + a 2b 4 5x 3 y 7x 2 y 2 + 8 xy 3+ 15a b5 17a b 3 3 + 14ab 5 + b 6 5x 3 y 7x 2 y 2 + 8 xy 3 + y 4a 6 + 15a 5b + 9a 4b 2 17a 3b 3 + a 2b 4 + 14ab 5 + b 6 19. x + x 11x4 39. m4 5m4 + 18am3 7a 2m2 a 3m + a 4 5 x + x 2 + 34 4m4 + 18am3 7a 2m2 a 3m + a 4 x 4 + x 3 16x + x 2 + 34 x 4 + x 3 + x 2 16 x + 34 20. m 3110. 16 m2n 7mn2 + 3n314 b + a c d m3 m2n 7mn2 + 3n3 1 30 b + a c d a b c d + 30 24. EJERCICIO 245 32 31.1 2a6. 6 m +9 n21 2121 3 1 23a + ab b 2 + n + m n mn24355 28 2 +1 2 1 2 5 3 10 + 9 3 1 2 3 a + ab b 2 m + n + m n mn2435 6 45 2 8 3 2 1 2 2 = a + ab b 5 3 1 23 19 3 435 m + m n mn + 2n62 8 452. 15 3 2 1 342 5 7.a + ab b2 xy yz + 7 3 553 9 5 2 1 1a ab+4 2 135 + 5 14 2 8 xy yz +5 3965 2 23 4 2 140 a +ab = xy yz + 146 5 391 2 1 314 2a ab b 2 + = xy yz + 15 5914 6 585 33 251 238. x+ xyybc86 103.5 3 2 31 3 2 x+xy 2y 2 bc + ab + cd 5106 4 9 15 + 24 2 50 + 181+ 20 2 18 53 2 x +xy ybc + ab + cd4060 1030 4 939 2 6821 2 39 2 1721 23132=x +xy y =x +xy y ab +bc + cd40 6010 40 15104 30 9 5 9. a + a + 32 1 2 a4. a b 623 7 29742 1+a a a b + 8 10859 28 + 7 2 10 + 920 21 58 6+21 a3 + a a+a b+ 810 24109 2 15 2 19 1 38 1 =a +3 a a =a b+ 8 1024109 2 7 4 3 10 . m + 12 mn 32 n 5 23 275. 9 x 8y55 2 11 25 3 mn2 n3+m n+ y xy +9218 107 11 21 20 4+7 3 5 2 1 5 2 30 + 8 2 5 x y xy +3m3 + mn2 n + m n+ 9807 11 367218 538 2 53 51111 = x2 y xy + m3 + m2n +mn2 n3 + 9807 11 21 367 855 19 2 3 x 2 xy y +97 40 11 25. 3 435 32 4 137 811. x + x3y xy + y 12. a+ b c + d5473 258 95 2 21 5 4 7 1 1 7 x4 x y + xy 3 y+b c + d 83 620 8 9 835 4 3 3515 7 3 4 5 4 112 + 77 +18 +17x + x y x2y 2 xy +ya+bc+d54 821 6 2 208 9823 5 8 3 1 4 119 89 7= x 4 + x3y x2y 2 xy y= a+ b c+ d 54 8216220 89 8 1197 = a+ b c+ d 2208EJERCICIO 251.3 2 56. 5 21 2 1a a a b+ ab 8 6 84357 2 5 3 a2+ ab 6 a68 69 20 2 511 2 55 22 + 7 2 1+ 18 5 3a a=a aa b+ ab a24 6246 883 65 29 2 19 5 3= a b + ab a2.8a+ 6b588 3 61 3 559 19 a +b a 3 + a 2b + ab2 2 5 688316 130 + 3 1533 a+b5 =a+b52 5 2 5 2 35 2 21 7. mn +mn + mn3 62 2111433. x + x y 633 7 2 22m4 mn + mn37 2 89 x y92 3 20 49 2 2 3 + 2m4 +m n+mn +mn3 667 21 1156 9 x3 +x y 6 = x3 x2y 6 9 9 2 29 2 2 5= m4 + m3n m n + mn3 611 5694.a+ b c1 3 2 a + b c2 4 3 7 41 3 2 2 2 3 1 42 14+33+2 175 8. x y +x y + x y + xy 7 a+ b c= a+ b c8 143 3 2 43243 1 53 3 2 12 x x y + xy 4 27 89 2 515. m + n+ p 1 5 7 4 1 6 3 2 2 2 3 8 + 3 4 63 + 2 3 62 x x y+x y + x y +xy 28 14 3249m n+ p 1 5 7 4 5 3 2 2 2 3 11 4 6523561+ 2 113=x x yx y + x y +xy m+ n+p= m n+ p2 814 3 24 9 362 362 1 5 7 4 5 3 2 2 2 3 11 4=x x yx y + x y +xy 7 2 9 2 814 3 24 26. 7 5 2 4 212 69. x y+x y x 3y 3 x 2 y 4 + xy 5 + y 9 38 137 4 21 2 4 x6+x y x y xy 5 + y69 11 7 5 6 + 7 4 2 1 3 3 11+ 1 2 42 + 13 67 13 4 2 1 3 3 12 2 4 15 6 x6 + xy+x y x y x y + y = x6 + x5 y +x y x y x y +y 9 9 8111399811 131 3 7 25 27 3210. x x y +xy y 39 811 52 3 1 23x + x y xy 2 636 4 1+ 2 3 14 3 2 5 6 2 7 3 2 + 3011 21732 x x y+xy y = x3 x y xy 2 y 3 318811 5 188115 3 4 23 2 4 5 611.mn mn +n107 92 67 4 2 5 2 41 6 3m +mn mn n + 13 20143 52 6 6 + 7 4 2 6 + 5 2 4 5 3 6 3 2 6 13 4 2 11 2 4 2 6 3m +mn mn +n + = m +mn mn + n + 13 20 14 9 5 13 2014 953 57 47 3 2 1 2 31 512. 8 c + 22 c d+ 12c d + c d 2 3 d 355 45 3 2 33 5+c d + c d cd 4 d11 6 4 13 3 5 7 + 10 47 + 10 3 2 1 2 3 3 4 13 + 9 5 c +c d+ c d + c d cd d 35 822 12 2 4 39 317 4 17 3 2 1 2 3 3 4 22 5 = c5 +c d+c d + c d cd d 35 822122 439EJERCICIO 26Para los problemas 1 al 14 las literales toman los siguientes valores:a = 1 b = 2 c = 3 x = 4 y = 5 m = 3/2 n = 2/52. a + b331. a ab2+ 2b 3 + 5a 2b 6ab 2 3ab b 2 a + 3b3 + 5a 2b 6ab 2 a 3 + 5a 2b 6ab 2 + 3b 33 a 2 4ab b 2 = 13 + 5 12 2 6 1 22 + 3 23 = 1+ 5 2 6 4 + 3 8 = 12 4 1 2 2 2 = 1 8 4 = 11 = 1+ 10 24 + 24 = 11 27. 13. a 223 1 8. 3 m n + 4 mn 2 n 223 1 5 a b+ c 2 31 21 2 1 3 1 2 1 511 5 mn +mn + n + m3a b+ c= a b + c 6422 2 322 3 4+1 2 3+ 1 251 1 5 1 m n+ mn + m3 = m3 + m2 n + mn2 1 2 + 3 = 1 + 56 4 62 2 3 2 3223 5 3 2 3 2 27 5 18 3 41 2 + 10 7= + + = + + == =3 21 26 2 5 2 58 6 20 2 25 2227 3 12 675 + 150 + 48 873=+ + ==8 4 50200 2004. 3m 5n 2 2 m2 10n 2 8mn 9. a5 3a 2b 4 + b 5 2m2 15n 2 8mn 2m2 8mn 15n 222 a b + 5a b4 2 3 3 3 3 2 2 9 484 = 2 8 15 = 2 3 a a 4b2 + 5a 3b 3 3a 2b4 + b 55 2 2 5 5 4 105 9 24 1245 48 2427 = 15 14 22 + 5 13 23 3 12 24 + 25 = ==== 1 4 + 5 8 3 16 + 32 = 1 4 + 40 48 + 32 = 21 2 5 5 10 105. x 4 18x 2 y 2 + 15y 4 10. ab + 10mn 8mx16x y3 + 6xy 9y 4 3 15ab x 4 + 16x 3y 18x 2 y 2 + 6xy 3 + 6y 4 16ab + 10mn 8mx 3 2 3 = 4 + 16 4 5 18 4 5 + 6 4 5 + 6 543 2 2 3 4= 16 1 2 + 10 8 4 2 5 2 = 256 + 80 64 18 16 25 + 24 125 + 6 625= 32 + 6 48 = 74 = 256 + 5.120 7.200 + 3.000 + 3.750 = 4.926 3 11. a6. a 7am + m323+ 5am + 5m3 8a 2 m 2 11a 2b + 9ab 2 b 3 a 3 2am2 + 6m3 8a 2 m a 3 8a 2 m 2am2 + 6m3a 3 11a 2b + 9ab 2 b33 3 2 324 3 9 27 = 13 1112 2 + 9 1 22 23 = 13 8 12 2 1 + 6 = 1 2 + 62 2 2 2 48 = 1 22 + 36 8 = 79 81 4 48 18 + 81 19 = 1 12 + ==2 444 1 4 12. x642 271 2 2 537.a +ab b2 x x+385 36 81 1 21 4 2 2 53 a 2 ab + b x x x+610 643 6 8 4 1 2 7 82 1 2 1 2 11 1 4 2 2 53a + ab b = a ab b 2= 4 4 4 +6 8 10281064 36 81 11 2 1 2 4 32 20 3 96 256 80 + 9 12 1 2 2 = = 4 + =2 8 102 8 103 6 8 24 1 1 2 10 5 83231 77 = = = == = 9 85 2 4 52020 248 28. 3 2 2 213.x3+x yxy2 x 1 x5 16 5 14. a + a ax 3 + ax 2 3 33 21 35 6 x+xy +y 4 525 ax 1 + 9a x 3 a x 2 43 3 3 2 23 2 1 3 2 5 x 1 x 5 54 x 3 x + x yxy + ya +a a 41652556 1 3 21 2 1 3349 x 3 x3 + x y+xy +y ax ax 1 + a 4165255613 2 1 1 3 3 49 4 3 = 43 + 4 5 + 4 52 +5 = 14 14 1 + 14 16 525 5 61 154 125 3 49 + 30 18 + 245 257 = 64 +16 + 25 + =1 += == 8 17 304 16525 5 6 3030 = 16 + 15 + 20 + 5 = 56EJERCICIO 277. m + n pmn+p1. + ab + b 2 a2 2m 2n + 2pm+np a2 5b 2 a 2 ab + 4b 2m n + p0 a 2 + ab 4b 2 ab + 4b 28.9ax a 2x 2 5ax + 3a 22.a+8 1 9ax + 7a 2 + 25 x 2 25 x 2 6a 2 a+6 14 6a 2 + 25x 2 24 x 2 5ax 3a 2 14 139.5a 2 + 6a 4a3 13. x+ 4xy 2 8a + 6 2a 3 5a 2 + 2a 2 3 2a 3+ 5x 2 y+ y3 2a 3 + 5a 2 2a + 2 a 3 5a 2 + 2a 3 x 3 + 5x 2 y + 4xy 2 + y 3 5 x 3 9x 2+4x41 7x y2 11x 7x 4 3 6x 11x 4 + 2x 3 + 9x 2 + 6x 410.x 3 5x 2 y 4xy 2 y 3 11x 4 2x 3 9x 2 6x + 4 12x 4 + 2x 3 + 9x 2 + 6x 5x 3 12x 2 y 4xy 2 y 311. 35a 2b 7ab 2 11a3+ b3 7a 35a b + 8ab + 6 32 2 7a ab32+54. 3m n + 4mn n 3 235m4 7a 3+ ab 52 8a ab + b + 53233m n 4mn + 5n3 3 2 4n3+ 4n3 5m4 4n312. 11n4+ 14n2 25n + 85. 8a + 9b 3c6a 19n3 6n2 + 9n 4 7a 9b + 3c a 11n4 + 19n3 + 8n2 16n + 4 a5an5 7n3 + 4n6.a b +ca +bc 11n 19n3 8n2 + 16n 44 2a + b c a a2a + b c n5 + 11n4 26n3 8n2 + 20n 4 29. 20. x 4 6x 2 y 2 + y 4x 4 2x 2 y 2 + 32y 413. 6a 3m+ 5am36 + 8x y + 31y2 24 x 4 2x 2 y 2 32y 47a 5a m 11a m4 32 2 6m 4x 4 + 2x 2 y 2 + 32y 407a 11a m 11a m + 5am 6m 643 2 23421. 6n + n+ n254a4 8a 2m2+ m4+ 7n3 n2 8n 6 7a 4 + 11a 3m + 11a 2m2 5am3 + 6m4 + 6 6n5 + n4 + 7n3 8n 6 6a 4 + 11a 3m + 3a 2m2 5am3 + 7m4 + 6 6n5 + n4 + 7n3 8n 6 4x 4 y + 13x 2 y 3 9xy 4n 6+ 3n4 + 8n3 1914. 6x5 + 8x y3 2+ xy 4 2y 5n 6n + 4n + 15n 8n 256 5 43 6x 4x y + 8x y + 13x y 8xy 2y54 3 22 34522. a5 3a 3b2 + 6ab 4 x5 30x 3 y 2 + 40xy 4 + y 5+ 22a b + 10a 3b2 11ab 4 b546x 5 + 4x 4 y 8x 3 y 2 13x 2 y 3 + 8xy 4 + 2y 5a 5 + 22a 4b + 7a 3b 2 5ab 4 b 57x 5 + 4x 4 y 38x 3 y 2 13x 2 y 3 + 48xy 4 + 3y 5a 5 + 22a 4b + 7a 3b2 5ab 4 b 515. a + b 2a 5a b4 + 7a b 2 3 b5ab 2a + ba 5 + 17a 4b + 7a 3b 2 + 7a 2b3 5ab 4 2b 52a b16. 8x +9 8x + 6y + 46y 5223. 4m3 5m2 2m 3m3 5m2 + 6m + 48x + 6y + 48 x + 6y + 6 7m3+ 8m + 4 m4 517. x2 6y2 x 7 xy + 34y 2 2 3m 5m + 6m + 432m 3m 5m + 6m 1 4 32 7 xy + 40y 29y 2 1624. 7a 2 11ab + b 22b 2 8x 2 7 xy + 34y 2 x 2 7 xy + 43y 2 16 7a 2 + 11ab + b 2 8 +418. 4a + 8ab 5b22 5a + ab + b22 2b 2 8 2b 2 4 a 2 7ab + 6b 2 4a 2 ab + b 225. 3a 4b + 5c5a 2 + ab + b 2a2+ 2b 2 7a + 8b 11 5a + 6b 2c 11 a + 2b 7c a + b + 2c19. x 3 y3 5a + 6b 2c 11 6a + 7b 11 14x y + 5xy2 2x 14x 2 y + 5xy 2 y 3326. 5a 3 + 14a 2 19a + 8a5 + 9a 1x 14x y + 5xy y3 22 3 a4 + 3a 2 13x 3 19y 3a a5 4+ 5a + 17a 10a + 6324x 3 14x 2 y + 5xy 2 20y 3 a 4 + 3a 3 5a 2a + 8a + 17a 10a + 15 4 3 2 30. 27. m4 + 10m2n2 + 15n4 5 + y5 29. x 11m n 14m n 3mn + n4 32 2 3 3x y + 21x y + 18x y y 5 4 3 2 2 3m 11m n 4m n432 2 3mn + 16n3 4x 5 + 3x 4 y + 21x 3 y 2 + 18x 2 y 36m4 + 7m2n2 + 8mn3 n4 x 5 + 32x 4 y 26x 3 y 2 + 18x 2 y 3 2xy 4 + y 5 m + 11m n + 4m2n2 + 3mn3 16n4 4 3 x 5 3x 4 y 21x 3 y 2 18x 2 y 35m + 11m n + 11 n + 11mn 17n4 m 3 2 23 4 29x 4 y 47x 3 y 2 2xy 4 + y 528. a5 + 4a 3b 2 + 8ab 4 b5x 1 30. 3a + 6ax 7a b 4+ 15a b 25ab + 3b 2 34 5a x 7a x 1 + a x 2 a 3b2 + 3a 2b3 5ab 44a x a x 1 + a x 2a 5 7a 4b + 3a 3b2 + 18a 2b 3 22ab 4 + 2b 58a x + 2 7a x + 1 a x+ 12 a x 13a 5 6a b 21ab2 3 4 6 4ax + ax 1 ax 2 a + 7a b 3a b 18a b + 22ab 2b54 3 22 3 4 58a x + 2 7a x + 1 5a x + 13 a x 1 a x 22a + 7a b 3a b 24a b + ab 5 4 3 2 2 34 2b 6 5EJERCICIO 281. x 2 +5 x4 x 2 + 2x 1 6. a2 x 3x 3 5a 2 x + 11ax 2 11x 32x 6 x+62 a 3 + 3ax2a 4a 2 x + 6ax 2 + 8x 33 x + 2x 122 x + 2x 3 2a 3 + a 2 x + 3ax 2 3x 3a 3 9a 2 x + 17ax 2 3x 32. 3a 5b + c 7a + b 4a 6b 2ca b 3c 8b 3c 7a + 7b + 3ca 3 + a 2 x + 3ax 2 3x 3 a 3 + 9a 2 x 17ax 2 + 3x 3 4a 6b 2c7a 7b 3c 3a + b + c10a 2 x 14ax 23. x 3+19x + 46x 3 x 2 +8 5x 3 x 2 + 7 3x 2 x + 1 3x 2 8x 5 6x x + 832 3x + 8 x + 5 26x + 2x 2 8x + 33 7. x4 + x23a +1 2 a 4 +2a +a32 x 3 3x + 5 7 x 3 + 8x 2 3x + 44. a31a 2 a4 ax 4 5x + 4 x2 x 4 3 a3 + a2 a4 + a a4 + a3 + a2 a 2x x 4 x + x + 2432x 7 x + 8 x 3x + 1 4 325. ab + bc + ac 5ab 3bc + 4acab 6bc + 9ac 92x 4 x 3 4 x 2 + x + 2 7bc + 8ac 9 ab + 3bc + 5ac 4ab 9ac x 4 + 7 x 3 8x 2 + 3x 1 ab 6bc + 9ac 94ab+ 9ac 3ab 6bc 9x 4 + 6x 3 12x 2 + 4x + 1 31. 8. m 4 n417m n 4m n 7mn3 3 2 2 m4 +617m3n + 2m2n2 7mn3 81n4 m4+ 6m2n2 80n4 m2n2 + mn3 4 m4+ m2n2 mn3 217m3n + 2m2n2 7mn3 81n4 m4 m2n2 + mn3 + 2 m4 + 17m3n + 3m2n2 8mn3 81n4 29.+ a3+ a 7 a a5 4 6a 2+ 8 a 4 4a 3 + a 2 a 5 a 4 + a 3 11a 2 10a + 27 5a 2 11a + 2616a 3 8a 2 7a 15 + a 4 12a 3 + 7a 2 + 7a + 15 a 5 a 4 + a 3 11a 2 10a + 27 a 4 + 12a 3 7a 2 7a 15 a5 11a 3 4a 2 3a + 4210. 3x 2 y2x 2 3xy y 2 20x 2 11xy + 8y 2 11xy + 9y 14 2 19x 8xy + 9y22 3x 2 + 11xy 8y 2 + 143x 2 11xy + 8y 2 1420x 2 11xy + 8y 2 17 x 2 + 1411. a 1a2 312.a 2 ab + b 2 a +1 a 43a 2 8ab + 7b 2 a 2 + 9ab + 3b 2 a 2 + ab 4b20 3a + 8 5a + 11ab 17b 2 2 8ab 7b 2 a 2 2ab + 9b 2 a 2 2a + 1 a 2 + 2ab 9b2 a 2 + ab 4b 2 ab + 5b 213. m4 1 m3 + 8m2 6m + 5m5 16 m5 16m4+ 7m2 19 m 7m + 1 2 16m + 7m 3 42 m + m 7m2 + 13m 543m4 m3 + 7m2 13m + 5 m5 16m4 + 7m2 19m5 17m4 + m3+ 13m 2414. x5 y5 2x y + 5x y 7 x y43 2 2 3 3y 5 7x 4 y x 3 y 2 + 11xy 4 x 5 + 2 x 4 y + 2 x 3 y 2 + 7 x 2 y 3 6 xy 4 + 4y 5 + 8 7x y 3 2 + 6 xy 4 8 xy 41 7x 4 y x 3 y 2 + 10xy 41x 2x y 2 x y 7 x y + 6xy 4y 85 43 2 2 345 7 x y x y + 10xy 1 4 3 24 x + 9x y + x y + 7 x y + 4xy 4 + 4y 5 + 7 54 3 2 2 315. a+ 7a 4 8a6 3a5+ 11a 3 a 2 +4 6a 4 11a 3 2a + 8 3a 4+ 7a 2 8a + 55a 5 3a 4 7a 3 + 48a 2 58a + 13 5a 3+ 5a 4a + 1 25a 5 7a + 41a 50a + 8 32 a + 3a 5 a 4 + 5a 3 4a 2 + 14a 136 a 6 3a 5 + a 4 5a 3 + 4a 2 14a + 13 5a 5 3a 4 7a 3 + 48a 2 58a + 13a 6 + 8a 5 4a 4 2a 3 + 44a 2 44a16. a5 7a 3 x 2 + 9+ 18a 3 x 2 4x 5 8 20a x4+ 21a x 19ax 2 34 9a x 17a x + 11a x 4 3 22 3 + 9a 3 x 2 7ax 4 + x 5 80a5 + 36a 20a x + 2a x + 21a x 26ax + x 71543 22 3 45a 9a x + a x 5 4 3 2 + 11a x 4 x2 35+ 28 a 5 9a 4 x + a 3 x 2 + 11a 2 x 3 4 x 5 + 28 a + 20a 4 x 2a 3 x 2 21a 2 x 3 + 26ax 4 x 5 + 71 511a 4 x a 3 x 2 10a 2 x 3 + 26ax 4 5x 5 + 99 32. EJERCICIO 29 77 4 325. 12 a 4 a a3 + a2 61 312 751. a +b a3 3 2 2 3 41 12 4 a + a 6a a+ 23 15 7545 3 a + b a b7 4 3 3 2 27+9 4 3 3 2 2 118 1 34 34a a + a 6 a a + a a 127 5127 55 3 322+394 5 a+ b a b 4 4 3 3 2 2 = a a + a 1 a173412 4 37 55 31 5 55 = a+ b=a b3 4124 121 5 26. x+ y z y 234 9 5 31 3 3 2 12 1 5 132. a6a + ay z +3x y+z 3 82595 2 9 20535 3 3 2 3 a3 + a2a a a+6 16 15+8 1132 + 156565 8 x+y z+3 x+z5333+5 33 2 9 20 2205 a3 + a2 + a 6 a a+6 1513 1 1317658 6 8= x+ yz+3= x+z4 3 2920 2 20 5= a3 a + 63 8 3 7 3 233. a +3b a+b +6 7. a b + ab2 b3 5 3 24 2 2 111 252 3 a b+6 a+ba b ab 2+ b 5 3 56863 529 2 3 114 + 112 1 2 9 10 2 3 2 3 a+b+6a+b+6 a b+ab b5 3 56 8 123372511 11 = a+ b+6 = a+ b+6 = a 2b ab 2 b 35352 8123 1 3 1 3 a b 2 3 1 33 214. 3 x 7x+ 5 11 2 a b+ 1 1 ab 2 + b 3 812 31 2 2x x+61 3 11 21 149 a + a b+ab 2 28 12 1 3 6 1 2 21+ 30 x x x+ 3 14 951 3 5 2 2 31 = x x x+ 1 221 1 133 149 5 8. a b b +c a+ b c2 935 2 951 351 11 5 3 xb c b c bc 63 59 10 9 10 1 35 2 231123365 2 1 1 6 +1 x +x + x a b cb+ c a c 3 149 5 2 9 5 910 2105+2 3 5 2 21 1 3 1 1 1 7 x +x + x 31= a+ b c = b+c= a c 6 14 95 2 9 5 910 210 7 3 5 2 2 = x +x + x6 5 1 614 9 33. 1 3 1 2 11 2211 319 2219. 3 a + 8 a + 54a 3 a+43 a 40 a 3a +83 31 1 3 29 2 1119 231 a2 aa a a3 + a +a 5 4 10 3 40 83404 101 3 5 24 2 32 11 3 10 29 2 22 189 10 8a + a a+a + a a+a+3 40410 3403812 801 3 19 2 3 1 1 3 19 2 2 112 1 1= a a a+ = a a a+ =a+ = a+3 404 10 3403 8 1280 12403 2 5 2 2 2 212 23 2 713 2110. 5 x 6 xy +9y9x+ 9 xy 3y 5 x + xy +36 y+23 1 1 17 2 22 3 2 13 2 7 11 xy y2 +x xy y x xy y 2 +2 3 4 459 2 253943 2 10 + 18 23 2 110 + 17 2 1 22 4+9 2 1 39 2 2 2 + 1x xy +y + x +xy y y +5 12 9 4 45 9 6 2 18 43 2 281 2 127 2 2113 2 1 37 2 3= x xy y + = x xy y =y +5 12 9 4 45 96218 43 2 7 1 2 13 2 713 2 1= x xy y + = x xy y 5 3 94 53622 1 31 21 2 13 2 3 3 73 a b + a b + ab 2 b 3 11. 7 a 5b 24ab54 8 210 331 3 5 1 2 312 3 3 1 3 a 2b + ab 2 + b a 2b + ab b 3 a 3 + a 2b ab 2 +b 48 10 4 8 227 4 8102 3 3 23 2 1 325 22 +1 2 3 3 2 + 5 2 315 1 3 7a a b + ab 2 b a b+ab b a b 74 8 104 82107 10 102 3 3 23 21 3 3 23 2 3 3 7 2 3 14 3 72 3 7 3 7= a a b + ab b = a b + ab b = a b = a b 74 8 10 482 10 7 10 10 75 10 1 2 2112.mn mn3 n4 34 2 4 3 2 2 2 5 4 5 42 m + m3n mn+ n m n4 7 5 5 3145 1 47 31 2 2 2 4 5 4 1 311 2 2 1 m mn + mn nm m nm n + mn314 204 3144 6044 + 1 4 12 7 3 20 24 + 15 2 2 135+2 4 1 3 11 2 2 1 2 m +m n+ m n mn3 n m nm n + mn3 n4 142060 43 4604 5 5 4 5 3 11 2 2 1 0=m +m n+m n mn3 n414 2060 4 3 5 4 1 3 11 2 2 1=m + m n+ m n mn 314 4 60 4 34. 1 113. x+ y2 3 3 1 y z 4 6 21 z +m 5 541 1311371 1 3 m+ n+ xyz+ m n 2 3821230 4 3 814+95 121 2 13 113 71140 3x+ yz+m + n+ xyz+ m n +2 12304382 1230 4381 1371 1 3 113 7 1 1 37= x+ y+z m + n+= xy z+ m n +2 1230 4 3 8 212 304 385 4 1 3314. a + a a6 25 2 2 3 a a +5 3 83 4 3 31 2 2 11 41 3 1 2 152 a a+ a a a a +8 46 3 24 122 331 339 31 33+ a+a+ a4+a 640 1112820 9 4 6 9 + 2 3 4 1 2 24 + 15 39165 22 + 911 24 41 1216 99.a + a a a+a a2 +24 12640 3324 2 26411 4 1 3 3 2 0152 11 4 1 3 1 2 152 .13 4 1 2 1117=a a a a+=a a a +=a a +24 12 6 40 33 24 12 2 33242264EJERCICIO 301. x3 x2+5 4. x 3 4x 2 +87. 5a + 8ab b 113 2 3 x + x + 3x 5 632 x 3 + 4 x 2 + x 13 a3+ b33x 6x 5 4a 3 + 8ab 2 11 Rta. x + x + 3x 11 32Rta. x 4 x x + 1332Rta. 5a + 8ab b3 1132 1 12. 5a + 9b 6c5.m4 3mn3 + 6n48.x y4 2 3 5a 9b + 6c + 8x + 9 m4 + 4m2n2 + 3mn3 6n4 81 1 x+ y 8x + 9 4m2n2 8 2 3 Rta. 5a 9b + 6c + 8x + 9 Rta. m 4m2n2 3mn3 + 6n4 + 84 4 1 13. a3 b3 6. 4x + 5x 5x 232Rta. x y4 2 3 a 3 8a 2b + 5ab2 3b3 5x 2 4 x + 8 8a 2b + 5ab2 4b 34x 3 9x + 6 Rta. a 8a b + 5ab 3b3 22 3Rta.4x 3 + 5x 2 5x 2 35. 9. 5x 2 7 xy 8y 2 10. n311. 0 5x + 7 xy + 8y + 12 2 9m + 8m n 5mn + n3 2 23 a + 5a 831 9m + 8m n 5mn + 2n3 2 23 a 3 + 5a 8 Rta. 5 x + 7xy + 8y + 12 210m 8m n + 5mn 2n3 2 23Rta. 0m3Rta. 10m3 8m2n + 5mn2 2n3EJERCICIO 311. x ( x y) 6. a + (a b) + ( a + b)11. x + y + ( x y + z ) ( x + y z) = x x+ y = a + ab a+b= x+ y+ x y+ z x y+ z =y= 2a a = a= x y + 2z(2. x + 3x x + 522) 7. a + b + 2a a b2 22 2212. a (b + a ) + ( a + b) ( a + 2b) = x 3x x + 52 2 = a b + 2a a + b2 2 2 2 2= a b a a + b + a 2b = 3x + 5= 3a a = 2a2 2 2= 2b3. a + b ( 2a + 3) 8. 2a { x + a 1} {a + x 3}() (13. x 2 y 2 + xy + 2 x 2 + 3xy y 2 + xy ) [ ] = a + b + 2a 3= 2a + x a + 1 a x + 3= x + y + xy 2 x + 3xy + y xy 22 2 2 = 3a + b 3= 1+ 3= 4 = 3x 2 + 3xy + 2 y 24. 4m ( 2m n)2 2 2(9. x + y x + 2 xy + y + x + y 2 22) [ ] 2 [ 2 2]{14. 8x + 2 xy + y x + xy 3 y x 3xy2 2} ( ) = 4m + 2m + n= x + y x 2 xy y x + y2 2 2 2 2 2 = 8x 2 xy + y + x xy + 3y x + 3xy 22 2 2 2 = 6m + n = x 2 xy + y2 2= 8x 2 + 4 y 25. 2 x + 3 y (4 x + 3 y)10. ( 5m + 6) + ( m + 5) 615. (a + b) + ( a b) ( b + a ) + (3a + b) = 2 x + 3y 4 x 3 y = 5m + 6 m + 5 6 = a b a b + b a + 3a + b = 2x = 6m + 5 =0EJERCICIO 32[1. 2a + a (a + b) ] [2. 3x x + y (2 x + y) ] [ 3. 2m (m n) (m + n)][ = 2a + a a b ] [= 3x x + y 2 x y] [= 2m m n m n] = 2a + a a b = 3x x y + 2 x + y= 2m m + n + m + n = 2a b = 4x= 2m + 2n 36. [() (4. 4 x + x xy + 3 y + 2 xy 3x + y2 22 22 ) ( )][11. ( a + b) + (a + b) ( 2a + 3b) + ( b + a b)][ = 4 x + x + xy 3 y + 2 xy + 3x y2 2 2 22 ][ = a b + a b + 2a 3b b + a b] = a b a b + 2a 3b b + a b = 4 x 2 x 2 + xy 3 y 2 + 2 xy + 3x 2 y 2 = 3a 7b = 6 x 2 + 3xy 4 y 25. a + {( 2a + b) ( a + b c) + a} {[12. 7m m + 3n 5 n 3 + m2 2 2() ()] } (2n + 3) = a + { 2a + b + a b + c + a} {[ = 7m2 m2 + 3n 5 + n + 3 m2]} 2n 3 = 7m { m 3n + 5 n 3 + m } 2n 3 = a 2a + b + a b + c + a 222 =a+c = 7m2 + m2 + 3n 5 + n + 3 m2 2n 3[6. 4m 2m + (n 3) + 4n (2m + 1)] [] = 7 m2 + 2 n 5[ = 4m 2m + n 3 + 4n 2m 1] [ ] = 4m 2m n + 3 4n 2m 1 {[13. 2a ( 4a + b) 4a + (b a ) ( b + a )]} = 5n + 2 {[ = 2a + 4a b 4a + b a + b a ]} = 6a b { 4a b + a b + a}[ (7. 2 x + 5x 2 y + { x + y} )] = 6a b 4a + b a + b a[ = 2 x + 5x ( 2 y x + y ) ]=b[ = 2 x + 5x + 2 y + x y ] = 2 x 5x + 2 y + x y = 2x + y ( [ {14. 3x 5 y + 2 x + y (6 + x) ( x + y)}])( [ = 3x 5 y + 2 x + {y 6 x} + x y ]){ [8. x 7 xy + y + x + 3xy 2 y 22( 22 )] }= 3x (5 y + [ 2 x + y 6 x + x y] ) = 3x (5 y 2 x + y 6 x + x y){ [ = x 2 7 xy + y 2 x 2 + 3xy 2 y 2]} = 3x 5 y + 2 x y + 6 + x x + y = x 2 { 7 xy y 2 x 2 + 3xy 2 y 2 } = 5x 5y + 6 = x 2 + 7 xy + y 2 + x 2 3xy + 2 y 2 = 2 x 2 + 4 xy + 3y 2[{15. 6c (2a + c) + (a + c) 2a (a + c) + 2c} ][ = 6c 2a c + { a c 2a a c } + 2c][ {9. (a + b) + 3a + b 2a + b (a b) + 2a }][ = 6c 2a c a c 2a a c + 2c ][ = a b + a + b { 2a + b a + b}] = 6c + 2a + c + a + c + 2a + a + c 2c[ = a b + a + b + 2a b + a b ]= 6a + 7c = a b a + b + 2a b + a b = a 2b( ) [ {16. 3m + n 2m + m + 2m 2n 5 ())} (n + 6)]( = 3m n [ 2m + { m + (2m 2n + 5)} n 6]{10. ( x + y ) 4 x + 2 y + x y ( x + y )[]} = 3m n [2m + { m + 2m 2n + 5 } n 6] = x + y {4 x + 2 y + [ x y x y ] } = 3m n [2m m + 2m 2n + 5 n 6] = x + y {4 x + 2 y x y x y} = 3m n 2m + m 2m + 2n 5 + n + 6 = x + y 4x 2 y + x + y + x + y = 6m + 2n + 1 = 3x + y 37. {[()]17. 2a + 5b + (3a c) + 2 a + b (c + 4) ( a + b) }[ {( ) [ ( ) ( 23. x + x + y x + y z x + y y )] }]= [ x + { x y [ x + y z + x y ] y}]= 2a + { [5b + 3a c + 2 ( a + b c 4) ] + a b}= 2a + { [5b + 3a c + 2 + a b + c + 4] + a b}= [ x + { x y + x y + z x + y y}]= 2a + { 5b 3a + c 2 a + b c 4 + a b}= [x x 2 y + z ]= 2a 5b 3a + c 2 a + b c 4 + a b= x + x + 2y z = 2y z= a 5b 6[ { () ( ) [ ( ) ] }] 24. a + a + a b a b + c a + b[()] {18. 3x + x (2 y 3) + (2 x + y ) + ( x 3) + 2 ( x + y) }= [ a + { a + a b a + b c [a + b] }]= [ 3x + ( x 2 y + 3)] + { 2 x y x 3 + 2 x y}= [ a + { a c a b}][]= 3x x 2 y + 3 2 x y x 3 + 2 x y= 3x + x + 2 y 3 4 x 2 y 1= [ a a c a b ] = 3a + b + c=4 EJERCICIO 33[][ ] {[19. ( a ) + ( a ) + b + c + ( c)] [ ]}[ ] {[ ]} = [a] a + b c c 1. a b + c d = a + a + {b c + c} (= a + b+ c d ) = b c+ c 2. x 3xy y + 62 2 =b = x 2 + ( 3xy y 2 + 6){[ ]} { [20. (a + b) + ( b a) (a + b)]}3. x 3 + 4 x 2 3x + 1 = { [ a b] } { + [ b + a] } a b= x 3 + ( 4 x 2 3x + 1) = {a + b} {b + a} a b 4. a 3 5a 2b + 3ab 2 b 3 = a b b a a b = a 3 + ( 5a 2b + 3ab 2 b 3 ) = 3a 3b 5. x x + 2 x 2 x + 1 4 3 2{[]} { []} [ {21. (a + b c) + (c a + b) + a + ( b)}]= x 4 x 3 + ( 2 x 2 2 x + 1) = { [ a b + c] } {+ [ c + a b] } + [ { a b}] 6. 2 a + b c + d [ = {a + b c} { c + a b} + a + b ] (= 2a b + c d ) = a b+ c+ c a+ b+ a+ b = a + b + 2c7. x + x + 3x 4 3 2 = x 3 ( x 2 3x + 4)[ {22. 3m + m n m + 4( ( ))}+ { (m + n) + ( 2n + 3)}] 8. x 3 5 x 2 y + 3 xy 2 y 3 = [ 3m + { m (n m 4)} + { m n 2n + 3}] = x 3 (5x 2 y 3xy 2 + y 3 ) = [3m + { m n + m + 4} m n 2n + 3 ] 9. a x 2 xy y 2 2 2 = [3m m n + m + 4 m n 2n + 3] = a 2 ( x 2 + 2 xy + y 2 ) = 3m + m + n m 4 + m + n + 2n 3 = 2m + 4n 7 10. a + b 2bc c2 22= a 2 ( b 2 + 2bc + c2 ) 38. EJERCICIO 341. x + 2 y + ( x y ) 6. 2a + ( 3a + b) [= x 2 y (x y) ] [= 2a ( 3a + b) ]2. 4m 2n + 3 ( m + n) + (2m n) [= 4m 2n 3 + ( m + n) (2m n)]2( 7. 2 x + 3xy y + xy + x + y2) (22)[= 2 x 2 3xy + ( y 2 + xy) ( x 2 + y 2 )]3. x 3xy + x xy + y 2 [( ) ]2 2= x2 {3xy [( x xy) + y ] }2 2 8. x 3 3x 2 + 4x 2 []4. x 3 3x 2 + 4 x + 2 3x 2 x + 3( ) = x 3 + 3x 2 + 4 x 2{ } [[ ]= x 3 3x 2 4 x + 2 + 3x + (2 x + 3) ] {[ ( )] }5. 2a + 3b 2a + a + b a 9.[m (3m + 2m + 3)]+ ( 2m + 3) 42 = { [ m (3m + 2m + 3)] ( 2m + 3)}= 2a [ 3b + { 2a + [a + (b a )] }]4 2EJERCICIO 35 17. ambn ab = am + 1bn + 11. 2 3 = 6 18. 5ambn 6a 2b3 x = 30am + 2bn + 3 x2. 4 8 = 32 19. xmync xmync x = xm + myn + nc1+ x = x 2my 2nc1+ x3. 15 16 = 240 20. mxna 6m2n = 6mx + 2na + 14. ab ab = a1+ 1b1+ 1 = a 2b25. 2x2 3x = 6x 2 + 1 = 6x3 EJERCICIO 366. 4a 2b ab 2 = 4a 2 + 1b1+ 2 = 4a 3b37. 5x 3 y xy 2 = 5x3 + 1y1+ 2 = 5x 4 y 3 1. am am + 1 = am + m + 1 = a 2m + 18. a 2b 3 3a 2 x = 3a 2 + 2b 3 x = 3a 4b3 x2. xa x a + 2 = x a + a + 2 = x 2a + 29. 4m2 5mn2p = 20m2 + 1n2p = 20m3n2p3. 4anb x ab x + 1 = 4an + 1b x + x + 1 = 4an + 1b 2 x + 110. 5a y 6x = 30a x y 22 2 2 4. a n + 1b n + 2 a n + 2b n = a n + 1+ n + 2 bn + 2 + n = a 2n + 3b 2n + 211. x 2 y3 4y3 z4 = 4x2 y 3 + 3 z4 = 4x2 y 6 z4 5. 3an + 4bn + 1 4an + 2bn + 3 = 12a 2n + 6b2n + 412. abc cd = abc1+ 1d = abc 2d 6. 3x 2 y 3 4x m + 1y m + 2 = 12x 2 + m + 1y 3 + m + 2 = 12xm + 3 y m + 513. 15x 4 y3 16a 2 x 3 = 240a 2 x 4 + 3 y 3 = 240a 2 x7 y 3 7. 4xa + 2b a + 4 5xa + 5ba + 1 = 20x 2a + 7b 2a + 514. 3a 2b3 4x 2 y = 12a 2b3 x 2 y 8. ambnc amb 2n = am + mbn + 2nc = a 2mb3nc15. 3a 2bx 7b3 x 5 = 21a 2b1+ 3 x1+ 5 = 21a 2b 4 x 6 9. xm + 1y a + 2 4xm 3 y a 5 c 2 = 4x2m 2 y 2a 3c 216. 8m2n3 9a 2mx 4 = 72a 2m2 + 1n3 x 4 = 72a 2m3n3 x 4 10. 5manb 1c 7m2a 3nb 4 = 35m3a 3n2b 5c 39. EJERCICIO 37 3 m2 3 1 3 m+1 3 1 2 4 31 44 528. a ab3 = am + 1b 3 =a b1. a a b = a 5b =a b = a 5b45 2 510 25 2 5 105 5 m n 3 3 2 7 2 3 9.a b ab 2c2. m n am610 714 1 1 1 37 2 5 21 2 5 3 2 5= am + 1 bn + 2 c = am + 1bn + 2 c = a m n=a m n=amn2 24 7 14 98142 x m +1 3 x 1 m 2 2 3 3 2 4 6 2 6 4210. a b a b3. x y a x y = a x y = a2x 6y 4 95 3 5155 2 1 2 x 1 2m + 1 2 2 x 1 2m + 1= ab=ab 1 3 4 4 3 24 3 5 5 1 3 5 53 5 154. m n a m n =amn =amn 8 540 10 3 m n4 12 3m 2n 3 3m 2n7 2 314 4 111. a b a 2mbn = a b =a b5. abc a = a bc = a 4bc 85 40108 756 42 x +1 x 3 244 x 3 2 3 3 45 31 12. a b c a b6. x y a 2by 5 = a 2bx 3y 9 = a 2bx 3 y 9 11 7 56 62 48= 2 a 2 x 2b x 1c 2 = a 2 x 2b x 1c 2 133 m+1 1 m+1 777. a am =a= a 35 15 5EJERCICIO 38 3 31 x a 8. m 5a 2m am 5 101. a 3a a 2 = 3a1+ 1+ 2 = 3a 415 2 + x 3 +1+ a 3 x+2 a+4=a m =a m2. 3x 2 x 3 y a 2 x = 3a 2 x 2 + 3 +1y = 3a 2 x 6 y 50103. m2n 3m2 5mn3 = 15m2 + 2 + 1n1+ 3 = 15m5n4 9. 2a a 2 3a 3 4a = 24a1+ 2 + 3 + 1 = 24a74. 4a 2 5a 3 x 2 ay 2 = 20a 2 + 3 +1x 2 y 2 = 20a 6 x 2 y2 10. 3b 2 4a 3b ab 5a 2 x= 60a 3 + 1+ 2 b 2 + 1+ 1x = 60a 6b 4 x5. am 2ab 3a 2b x = 6am +1+ 2b1+ x = 6am + 3b x + 1 1 3 2 23 6 2 + 4 3 +1 1 11. a mb x a 2 2ab 3a 2 x6. x a x a 4m =a x m = a 6 x 4m 2 35 30 5= 6a m + 2 + 1+ 2b x + 1x = 6am + 5b x + 1x 2 m 3 2 4 1 23 10 3 3 27. a a b 3a 4b x + 112. x y xy 2 x x y 3 4 253418 m + 2 + 4 4 + x + 136 2 + 1+ 3 + 2 1+ 2 + 1 3 8 4 =ab= a m + 6b x + 5 = xy= x y1228 4EJERCICIO 394. a 4a + 6a32 2. 8x 2 y 3y 23. x 4x + 321. 3x 3 x 2 2x2ax 3 2x3ab 6x + 2x4 316ax 5 y 6ax 3 y 2 2x 3 + 8 x 2 6 x3a 4b 12a 3b + 18a 2b 40. 5. a 2ab + b 2 213. x 3 3x 2 + 5x 6 ab 4x 2 a 3b + 2a 2b 2 ab 3 4 x 5 + 12 x 4 20x 3 + 24 x 26. x 6 x 8x5 314. a 6a x + 9a x 8 432 22 2 3a x 33bx 3a 2 x 7 18a 2 x 5 24a 2 x 33a 4bx 3 18a 3bx 4 + 27a 2bx 5 24bx 37.m4 3m2n2 + 7n4n+ 315. a 3a n + 2 4a n + 1 an 4m3 x an x 2 4m7 x + 12m5n2 x 28m3n4 x a 2n + 3 x 2 + 3a 2n + 2 x 2 + 4a 2n + 1x 2 + a 2n x 28. x 4x y + 6 xy32 216. x 4 6 x 3 + 8 x 2 7x + 5 ax 3 y 3a 2 x 3 ax 6 y 4ax 5 y 2 + 6ax 4 y 3 3a 2 x 7 + 18a 2 x 6 24a 2 x 5 + 21a 2 x 4 15a 2 x 39.a 5a b 8ab 3 2217. 3x + 5x y 7 xy 4y322 3 4 a 4m 222 5a xy 4a 7m2 + 20a 6bm2 + 32a 5b 2m2 15a 2 x 4 y 2 + 25a 2 x 3 y 3 35a 2 x 2 y 4 20a 2 xy 5m 110. a am + am 218. x a + 5 3x a + 4 + x a + 3 5x a + 1 2a 2x 2 2a m + 1 + 2a m 1+ 1 2a m 2 +1 2x a + 7 + 6x a + 6 2 x a + 5 + 10x a + 3= 2a m + 1 + 2a m 2a m 1m+1 19. a 8 3a 6b 2 + a 4b 4 3a 2b 6 + b 811. x + 3xm x m 1 2m 5a 3 y 23x 5a11y 2 + 15a 9b 2 y 2 5a 7b 4 y 2 + 15a 5 b 6 y 2 5a 3b 8 y 2 3 x 3 m + 1 + 9 x 3m 3 x 3m 1m 1 n + 2 m2 n+4 m 1 n +1 m2 n+ 220. a b + 3a b a b m n + a m 3b n + 612. a b + a b a b m n4a mb 3 3a 2b4a 2 mb n + 3 + 12a 2 m 1b n + 5 4a 2 m 2b n + 7 + 4a 2 m 3b n + 9 3a m + 2bn + 1 + 3am + 1bn + 2 3a mbn + 3EJERCICIO 4012 3 1 2 21 2a b23 a b+ c a2 + ab b 21. 2 3 2. 3 a 4 b3.565 4. 5 3 92 25 3a 2 xa2 3 ac 25 a b 3 3 6 2+23 62 1+ 2 4 215 1+ 1 2 510 2 + 1ax + a2 + 1bx a 2b 2 x aa b4 6 3 1+ 1 a c +abc 2 53 9 10 15 a3 + 1b +a b 1518 15ac91262 1 3 4 252 = a 4 x + a3bx a 2b 2 x = a a b4 41 3 2= a 2c 2 +abc 2 ac 3 53 515 = a b+ a b 18392 41. 1 2 2 1 1 2 1 2 1 2 1 25. x xy y 2a b + x y 354 23 4 55 3 3 a 2m y8 25 2+ 25 2 2 5 2 2 5 2 2 3 2 3 6 3 8. a m+ a b ma mx +a my x y xy 3 + 1 y 2 + 3 16243240 6 1085 4 5 2 2 5 2 2 1 2 2=a m+a b ma mx + a my 13 31624328 = x 2 y 3 xy 4 y 5 25 82 3 1 25 1 9. m + m n mn2 n36. 3a 5b + 6c 3 26 93 2 3 3 2 3 a x mn 10 4 9 2 + 1 3 15 2 3 18 2 3 6 3 + 2 3 3 2 + 2 1+ 3 15 1+ 2 2 + 3 3 2 3 + 3 a x + a bx a cx m n + m n m n mn10 1010 128 2436 9 3 3 3 2 3 9 2 31 351 =a x + a bx a cx= m5n3 + m4 n4 m3n5 m2n610 25 2 88 12 2 4 2 2 1 4 2 6 1 4 2 3 2 4 1 67. x x y + yx x y + x y y 9 3 53 510 3 3 4 5 x y a3x 4 y3 7 76 4 +3 4 3 2 + 3 2 + 4 3 3 4 + 410 3 6 + 4 3 5 3 4 + 4 2 + 3 15 3 2 + 4 4 + 3 5 3 4 6 + 3x y x y + x y10. a x y + a x y a x y +a x y 63 721 3521 3570 2 7 4 3 5 6 1 3 8 2 5 3 1 3 4 9 = x y x y + x y= a 3 x10 y 3 + a 3 x 8 y 5 a 3 x 6 y 7 +a x y 21777 21714EJERCICIO 411. a + 3 3. x + 5 5. x + 37. 3x 2 y a 1 x4x+52x + y a 2 + 3a x + 5x 2 x 2 3x6x 2 4 xy a3 4x 20 5x + 15 + 3xy 2 y 2 a 2 + 2a 3 x + x 20 2 x 2 8x + 15 6x 2 xy 2 y 22. a 3 4. m 6 6. a 28. 5x 4y a +1 m5a 3 3x + 2y a 2 3a m2 6ma 2 + 2a 15x 2 + 12xy a3 5m + 30+ 3a + 6+ 10xy 8y 2 a 2a 3 2m 11m + 30 2 a 2 + 5a + 6 15x 2 + 22xy 8y 2 42. 9. 5a 7b 11. a + b 13. 9m + 8na + 3b 8a 4b6m + 4n 5a 2 7ab 8a 2 + 8ab 54m2 + 48mn + 15ab 21b2 + 4ab 4b2 36mn + 32n2 5a 2 + 8ab 21b2 8a 2 + 12ab 4b2 54m2 + 12mn + 32n210. 7x 3 12. 6m 5n 14. 7y 32x + 4 mn2y 1114x 2 6x 6m2 5mn 14y 2 6y + 28x 12 6mn + 5n 2+ 77y + 3314x + 22x 122 6m 11 + 5n2mn 2 14y + 71y + 332EJERCICIO 421. x + xy + y 5. a + a a9. m m + m 22 2 3 2 3 2 xy a 1am + a x 3 + x 2 y + xy 2a 4 + a3 a2 am4 am3 + am2 2am x y xy y 2 2 3 a a 32+a + am3 am2 + am 2a x3 y3a4 2a 2 + aam4 am 2a6. m + m n + n10. 3a 5ab + 2b4 2 2 42. a 2ab + b222 2 a b m n 22 4a 5b a 2a b + ab3 22m6 + m4n2 + m2n412a 3 20a 2b + 8ab 2 a 2b + 2ab 2 b 3 m4n2 m2n4 n6 15a 2b + 25ab 2 10b 3 a 3 3a 2b + 3ab 2 b 3m6 n612a 3 35a 2b + 33ab 2 10b 37. x 2x + 3x 13 23. a + 2ab + b11. 5m 3m n + n2242 24 a +b2x + 3 3m n a 3 + 2a 2b + ab 22x 4 4 x 3 + 6x 2 2 x15m5 9m3n2 + 3mn4+ a b + 2ab + b223+ 3x 6 x + 9x 33 2 5m n 4 + 3m n2 3 n5 a 3 + 3a 2b + 3ab 2 + b 3 2x 4 x 3+ 7x 3 15m5 5m4n 9m3n2 + 3m2n3 + 3mn4 n512. a + a + 1 24. x 3x + 1 9. 3y 6y + 532 3 x+3 y2 + 2 a2 a 1 x 4 3x 3 +x 3y 5 6y 3 + 5y 2a 4 + a3 + a2+ 3x 9x 3 2 +3 + 6y3 12y + 10 a3 a2 a x4 9x 2 + x + 3 3y 5 + 5y 2 12y + 10 a2 a 1 a4 a 2 2a 1 43. 13. x 3 + 2x 2 x19. x 2 2xy + y 2 x 2 2x + 5 x 2 + xy + 3y 2 x + 2x x 54 3 x 4 + 2x 3 y x 2 y 2 2x 4 x + 2x4 3 2+ x 3 y 2x 2 y 2 + xy 3+ 5x + 10x 5 x 32+ 3x 2 y 2 6xy 3 + 3y 4 x5+ 12x 2 5x x 4 + 3x 3 y 5xy 3 + 3y 420. n 2n + 1 214. m 3m n + 2mn 322 m 2mn 8n 2 2 n2 1 m5 3m4n + 2m3n2 n4 2n3 + n2 2m4n + 6m3n 2 4m2n 3 n2 + 2n 1 8m3n 2 + 24m2n 3 16mn 4 n4 2n3+ 2n 1 m 5m n 54 + 20m n 16mn 2 3415. x 2 + x + 1 21. a 3a b + 4ab 322 x2 x 1a 2b 2ab 2 10b 3 a 5b 3a 4b 2 + 4a 3b 3 x4 + x3 + x2 2a 4b 2 + 6a 3b 3 8a 2b 4 x3 x2 x 10a 3b 3 + 30a 2b 4 40ab 5 x2 x 1 a 5b 5a 4b 2+ 22a 2b 4 40ab 5 x4 x 2 2x 116. x 3x + 2 4222. 8x 3 12x 2 y + 6xy 2 9y 3 x 2 2x + 32x + 3y x 6 3x 4+ 2x 216x 4 24 x 3 y + 12x 2 y 2 18xy 3 2x 5+ 6x 3 4x + 24x 3 y 36x 2 y 2 + 18xy 3 27y 4+ 3x 4 9x 2 +6 16x 4 24 x 2 y 2 27y 4 x 6 2x 5+ 6x 3 7 x 2 4 x + 623. 2y 3y + y 43217. m3 + m2 4m 1 2y + 5 m3 + 1 4 y 4 6y 3 + 2y 2 8y m6 + m5 4m4 m3+ 10y 3 15y 2 + 5y 20+ m3 + m2 4m 1 4y + 4y 3 13y 2 3y 204 m6 + m5 4m4+ m2 4m 124. a + 2ax + 3x 3 2 318. a 5a + 2 3 a a+5 2 2a 2 3ax x 2 a5 5a 3 + 2a 2 2a 5+ 4a 3 x 2 + 6a 2 x 3 a 4 + 5a 2a2 + 3a x 4 6a 2 x 3 9ax 4+ 5a3 25a + 10 +a x3 2 2ax 4 3x 5 a5 a4+ 7a 2 27a + 10 2a + 3a x + 5a x5 43 2 11ax 4 3x 5 44. 30. y 2y + 1225. x 4 3x 3 y + 2x 2 y 2 + xy 3 x 2 xy y 2y 4 2y 2 + 2 x 6 + 3x 5 y 2x 4 y 2 x 2 y 3y 6 2y 5 + y 4 x 5 y + 3x 4 y 2 2x 3 y 3 x 2 y 4 2y 4 + 4y 3 2y 2 x 4 y 2 + 3x 3 y 3 2x 2 y 4 xy 5 + 2y 2 4y + 2 x 6 + 2x 5 y 3x 2 y 4 xy 5 y 6 2y 5 y 4 + 4y 3 4y + 231. m 3m + 4 4226. a 3 5a 2 + 2a 3 a 2a 7 3 3m3 2m + 1 a 6 5a 5 + 2a 4 3a 33m7 9m5 + 12m3 2a 4 + 10a 3 4a 2 + 6a 2m 5 + 6m3 8m 7a + 35a 14a + 21 3 2+m 4 3m 2 +4 a 5a 65 + 31a 8a + 21 2 3m 11m + m + 18m 3m 8m + 4 754 3227. m + m m + 3 32. a + a a + 1 4 3 2 32 m 2m + 32a + a 2 2a 1 3 m6 + m5 m4 + 3m2a6 + a 5 a 4 + a3 2m5 2m4 + 2m3 6m+a + a5 4 a3 + a2 + 3m4 + 3m3 3m2 +9 2a 4 2a 3 + 2a 2 2a m6 m5+ 5m3 6m + 9 a 3 a2 + a 1 a 6 + 2a 5 2a 4 3a 3 + 2a 2 a 128. a 4 + a 3b 3a 2b 2 ab3 + b 433. 8x 12x y 6xy + y3 2 23 a 2 2ab + b2 3x 2 2xy + 4y 2 a 6 + a 5b 3a 4b 2 a 3b 3 + a 2b 4 24x 5 36x 4 y 18x 3y 2 + 3x 2 y 3 2a b 2a b + 6a b + 2a b 2ab54 2 3 32 4 5 16x 4 y + 24x 3 y 2 + 12x 2 y 3 2xy 4 + a b + a b 3a b ab + b4 2 3 3 2 4 5 6+ 32x 3 y 2 48x 2 y 3 24xy 4 + 4y 5 a 6 a 5b 4a 4b 2 + 6a 3b 3 3ab5 + b6 24x 5 52x 4 y + 38x 3 y 2 33x 2 y 3 26xy 4 + 4y 529. x 4 x 3 y + x 2 y 2 xy 3 + y 434. 5a 4a + 2a 3a 1432x 2 + xy 2y 2a 4 2a 2 + 2x x y+ x y 65 4 2 x y3 3 + x y2 4 5a 8 4a7 + 2a 6 3a 5 a 4 + x 5 y x 4 y 2 + x 3 y 3 x 2 y 4 + xy 5 10a 6 + 8a 5 4a 4 + 6a 3 + 2a 2 2x y + 2x y4 23 3 2x y + 2xy 2y2 4 5 6 + 10a 4 8a 3 + 4a 2 6a 2x6 2x 4 y 2 + 2x 3 y 3 2x 2 y 4 + 3xy 5 2y 65a 8 4a7 8a 6 + 5a 5 + 5a 4 2a 3 + 6a 2 6a 2 45. 35. x x + x x + 1 4 3 2 40. 3a 5 6a 3 + 2a 2 3a + 2x 2x + 3x + 6 32 a 4 3a 2 + 4a 5x7 x 6 + x 5 x 4 + x 33a 9 6a 7 + 2a 6 3a 5 + 2a 4 9a 7+ 18a 5 6a 4 + 9a 3 6a 2 2x 6 + 2x 5 2x 4 + 2x 3 2x 2+ 12a6 24a 4 + 8a 3 12a 2 + 8a+ 3x 5 3x 4 + 3x 3 3x 2 + 3x 15a 5 + 30a 3 10a 2 + 15a 10+ 6x 4 6x 3 + 6 x 2 6x + 63a 9 15a 7 + 14a 6 28a 4 + 47a 3 28a 2 + 23a 10x 7 3x 6 + 6x 5+ x 2 3x + 636. 3a + 2a 5a 4 41. a + b c32a + a 2a + 1 32ab+c3a 6 + 2a 5 5a 4 4a 3 a 2 + ab ac+ 3a 5 + 2a 4 5a 3 4a 2 ab b 2 + bc 6a 4 4a 3 + 10a 2 + 8a+ ac+ bc c 2+ 3a 3 + 2a 2 5a 4 a2 b 2 + 2bc c 23a 6 + 5a 5 9a 4 10a 3 + 8a 2 + 3a 437. 5y 4 3y 3 + 4y 2 + 2y42. x + 2y zy 4 3y 2 1 xy+z5y 8 3y 7 + 4 y 6 + 2y 5 x 2 + 2xy xz 15y 6 + 9y 5 12y 4 6y 3 xy 2y 2 + yz 5y 4 + 3y 3 4y 2 2y + xz + 2yz z 25y 8 3y 7 11y 6 + 11y 5 17y 4 3y 3 4y 2 2y x 2 + xy 2y 2 + 3yz z 238. m 2m n + 3m n 4n 43. 2x 3y + 5z 432 2 4 m3 + 3m2n 5mn2 + n3 x + y + 2z m7 + 2m6n 3m5n2 + 4m3n4 2x 2 + 3xy 5xz + 3m n 6m n + 9m n6 5 24 3 12m2n5+ 2xy 3y 2 + 5yz 5m5n2 + 10m4n3 15m3n4+ 20mn6+ m4n3 2m3n4 + 3m2n5 4n7+ 4 xz 6yz + 10z 2 m7 + 5m6n 14m5n2 + 20m4n3 13m3n4 9m2n5 + 20mn6 4n7 2x 2 + 5xy xz 3y 2 yz + 10z 239. x 6 3x 4 y 2 x 2 y 4 + y 6 44. x 2 xy xz + y 2 yz + z2x 2x y + 3xy 53 2 4x +y+zx11 3x 9 y 2 x 7 y 4 + x 5 y 6 x 3 x 2 y x 2z + xy 2 xyz + xz 2 2x 9 y 2 + 6x 7 y 4 + 2x 5 y 6 2x 3 y 8+ x2y xy 2 xyz + y 3 y 2 z + yz 2 + 3x 7 y 4 9x 5 y 6 3x 3 y 8 + 3xy10 +x z 2 xyz xz 2 + y 2z yz 2 + z 3x11 5x 9 y 2 + 8x 7 y 4 6x 5 y 6 5x 3 y 8 + 3xy10x3 3xyz + y3 + z3 46. x 1x2EJERCICIO 43 7. a + 3a 2a x x2 ax ax 1 + ax+ 2 x +11. a a + ax a 2x + 3a 2 x 1 2a 2x 2 a +1 a 2 x 1 3a 2 x 2 + 2a 2 x 3a x+ 3 a x +2+a x +1+ a 2 x 2 + 3a 2 x 3 2a 2 x 4 + a x + 2 a x +1 + a xa 2x + 2a 2 x 1 4a 2 x 2 + 5a 2 x 3 2a 2 x 4x+ 3a +a xa+4 8. m ma + 3 2ma + 2 + ma + 12. xn + 3 + 2xn + 2 + xn + 1 a3 ma 1 + ma 2 + mx +x2 m2a + 3 + m2a + 2 + 2m2a + 1 m2a x n + 5 + 2x n + 4 + x n + 3+ m2a + 2 m2a + 1 2m2a + m2a 1 x n + 4 + 2x n + 3 + x n + 2 + m2a + 1 m2a 2m2a 1 + m2a 2 x n + 5 + x n + 4 + 3 x n + 3 + xn + 2 2a + 32a + 2 m + 2m+ 2m2a + 1 4m2a m2a 1 + m2a 2a+ 2 a +1a 13. m + m m + ma m2 2m + 3 9. x a 1 + 2x a 2 x a 3 + x a 4 a3 ma + 4 + ma + 3 ma + 2 + ma + 1 xa 1 xa 2 x 2ma + 3 2ma + 2 + 2ma + 1 2ma x 2a 2 + 2x 2a 3 x 2a 4 + x 2a 5a+ 2a +1a 1+ 3m + 3m 3m + 3ma x 2a 3 2 x 2a 4 + x 2 a 5 x 2 a 6 ma + 4 ma + 3+ 6ma + 1 5ma + 3ma 1 x 2 a 4 2 x 2 a 5 + x 2 a 6 x 2a 7 x 2a 2 + x 2a 3 4 x 2a 4 x 2a 7n+ 2 n +14. a + 3a 2ann +1 a +an n 1 2n 2 3 n3 4 10. a b a b + 2a b a bn2n + 32n + 22n + 1a+ 3a 2aanb2 an 2b4 + a 2n + 2 + 3a 2n +1 2a 2n a 2nb3 a 2n 1b 4 + 2a 2n 2b 5 a 2n 3b6a 2n + 3 + 4a 2n + 2 + a 2n + 1 2a 2n a 2n 2b 5 + a 2n 3b 6 2a 2n 4b7 + a 2n 5b 8 a 2nb3 a 2n 1b 4 + a 2n 2b5 2a 2n 4b7 + a 2n 5b85. x a + 2 + 2x a +1 x ax a + 3 2x a + 1 11. a x + b xx 2 a + 5 + 2x 2 a + 4 x 2 a + 3 a m + bm2a + 3 2a + 22a + 1 2x 4x+ 2x am + x + amb x2a + 5x+ 2x 2 a + 4 3x 2a + 3 4 x 2 a + 2 + 2x 2 a + 1+ a x bm + bm + x m+ x a + a b + a xbm + bm + xm x x 1x26. a 2ax+ 3aa 2 + 2a 1x 1 n1 12. a bx+2 x +1a 2a+ 3a x abx +1 + 2a 4a x + 6a x 1 a x abn 1 x 1 x2 a + 2ax 3a a x 1b + bnx+2x 1x2a 2a + 8ax 3a a ab x n 1 a x 1b + bn 47. 13. 5a m + + a m + + 3a m2 2 2 126a 3m 1 8a 3m 2 + a 3m 3 30a 5m + 1 + 6a 5m + 18a 5m 1 + 40a 5m 8a 5m 1 24a 5m 2 5a 5m 1 + a 5m 2+ 3a 5m 3 30a 5m + 1 + 46a 5m + 5a 5m 1 23a 5m 2 + 3a 5m 3 a + 2 x 1 a +1 x a x +114. x y 4x y + 3x y 2x 2a 1y x 2 4x 2a 2 y x 1 10x 2a 3 y x 2x 3a + 1y 2 x 3 + 8x 3a y 2 x 2 6x 3a 1y 2x 1 4x 3a y 2 x 2 + 16x 3a 1y 2 x 1 12x 3a 2 y 2x 10x 3a 1y 2 x 1 + 40x 3a 2 y 2 x 30x 3a 3 y 2 x + 1 2x 3a + 1y 2 x 3 + 4x 3a y 2 x 2+ 28x 3a 2 y 2 x 30x 3a 3 y 2x + 1EJERCICIO 441 2 1 1 3. x xy + y 22 3 4 1 11. a b 23 2 3x y32 1 1 a+ b 2 32 2 2 3 2x x y+ xy 26912 1 2 1 a ab3 2 3 2 3 6 9 x y+xy y 3 4 6 8 1 1 + ab b22 3 8 + 27 22+6 2 3 3 4 6x x y+xy y6 36 128 1 2 49 1 a ab b 2 1 3 35 2 83 3 6 366= x x y+xy y23 36128 1 5 1 = a2 +ab b21 3 35 22 2 3 3 636 6= x x y + xy y3 363822. x y 1 2 254. a ab + b24 3 15 x+ y 13 36 a b42 1 22 x xy1 31 2 2 3 15a ab + ab216412510 2 +xy y 3 23 2 6 3630 ab +ab b82 6 1 2 4 25 10 2 x xy y 1 3 2+3 22 + 18 2 33030 a a b+ab b316812 1211 = x2 +xy y 21 3 5 220 2 3303 =a a b+ ab b3168 12 1 71 = x2 +xy y 21 3 5 25 3103 =a a b + ab 2 b168 3 48. 2 2 1 13 2 125. m + mn n2 6. x + x 5 3 284 5 3 2 1 m mn + 2n2 2x x + 23 236 4 3 3 3 2 2 6 5 2 4 4 3m + m n m n x + x x 1064 84 5 211 3 3 1 22 m3n m2n2 + mn 3 x x + x 5322412 15 422 46 22 4 + m2n2 + mn3 n+x+ x 53284 56 4 15 12 3 45 + 20 48 2 2 3 + 42 6 5 2 4 96 + 15 3 2 18 2 8 + 30 4m + m nm n +mn3 n4 x + x x x + x 10 30 6062 8412024 6056 43 3 17 2 2 7 3 5 1 4 111 3 16 2 38 4 =m +m n m n + mn3 n4= x + x x +x + x 10 30 60642120 24605 3 4 1 3 17 2 2 7 3 5 1 4 37 3 2 2 19 4 = m + m n m n + mn3 n4= x + x x + x + x 510 6064240 33052 3 1 1 2 11 3 x x2y + xy7. 2 x + 3 ax + 2 a 8.2 27 5 21 2 2 5 2x xy + y 3 2 2436 x ax + a 2 2 3 2 51 41 3 2 x x y+x y 3 4 3 39 2 2 28 208 x + ax + a x 4 42 3 22 2 3 46 4x y+ x y x y 21 1561 1 2 23 + ax 3 a x a3x10 3 25 2 352 32+ x y x y +xy 4 42 30 122 2 22 6 4 a x + a3x+ a2 5 x 21+ 80 4x y+ 105 + 112 + 200 3 2 10 + 5 2 3 5 x y x y +xy 469 6 28 420840 3012 3 4 3 + 3 3 27 4 4 2 2 27 4 3 6=2 5x 101 4 x y+417 3 2 15 2 3x y x y +5xy 4 x +ax + a x a x + a4 28 420 840 30 12 46121861 5 101 4 139 3 2 1 2 3 5 36 19 2 2 23 3 6 = x x y+ x y x y +xy 4 = x 4 + ax 3 +a x a x + a414 420 280212 46 12186 3 419 2 2 23 3 = x + ax +3 a x a x+a4 41218 1 3 1 2 119. x + x x+ 4 3 42 3 21 1 x +x 2 10 5 3 5 3 43 3 3 2 x + x x +x 8 68 41 41 3 1 21 +x + x x+x 40 3040 20 1 31 2 11 x x +x 20 1520 103 5 60 + 3 4 45 4 + 6 3 90 3 8 2 1+ 11x +x x + x +x8 120 12012020103 63 4 47 3 79 2 21 3 5 21 4 47 3 79 2 11 = x5 +x x + x +x= x +x x + x +x8120 120 120 2010 840120 120 1010 49. 3 1 2 110. 4 m 2 m n + 5 mn 4 n 3 2232 2 2 5m mn + n2332 6 5 2 4 4 3 2 2 2 3 m m n +m n m n12 615126 42 3 2 4 2 3 2 m n+m n m n +mn 4 1261512 15 3 2 5 2 3 105 5+m n m n +mn 4 n8 4 108 6 5 4+6 432 + 40 + 225 3 2 10 + 16 + 75 2 3 20 + 1205 m m n+ m n m n + mn4 n512 121206012081 5 10 4 297 3 2 101 2 3 1405 5 1 5 5 499 3 2 101 2 3 75 = m m n+ m n m n + mn n = m m n + 4m n m n + mn 4 n521212060 1208 2 640 6068EJERCICIO 454. m 5m n + 6mn + n por m 4mn n 3 2 2 3 3 2 31. x x + x por x 13 2 2 1 1+ 1 1 5 + 6 + 1 1+ 0 11 + 0 4 11 1+ 11 5 + 6 + 1 1+ 1 1 4 + 20 24 4 1 + 5 6 11 1+ 0 + 1 1 = x5 x 4 + x 2 x1 5 + 2 + 20 19 10 1 = m6 5m5n + 2m4n2 + 20m3n3 19m2n4 10mn5 n62. x + 3 x 5x + 8 por x 2x 7432325. x 8x + 3 por x + 6x 5424 2 1+ 3 5 + 0 + 81+ 0 8 + 0 + 3 1 2 + 0 71+ 0 + 6 + 0 51+ 3 5 + 0 + 8 1+ 0 8 + 0 + 3 2 6 + 10 + 0 16 + 6 + 0 48 + 0 + 18 7 21+ 35 + 0 56 5 + 0 + 40 + 0 151+ 1 11+ 3 13 + 19 + 0 56 1+ 0 2 + 0 50 + 0 + 58 + 0 15 = x 7 + x 6 11x 5 + 3x 4 13x 3 + 19x 2 56 = x 8 2x 6 50x 4 + 58x 2 156. a 6 3a 4 6a 2 + 10 por a 8 4a 6 + 3a 4 2a 23. a + 3a b 2a b + 5ab b4 3 2 2 3 4por a 2ab + b2 21+ 0 3 + 0 6 + 0 + 10 1+ 3 2 + 5 11+ 0 4 + 0 + 3 + 0 2 1 2 + 11+ 0 3 + 0 6 + 0 + 101+ 3 2 + 5 1 4 + 0 + 12 + 0 + 24 + 0 40 2 6 + 4 10 + 2 + 3 + 0 9 + 0 18 + 0 + 30+1 + 3 2 + 5 1 2 + 0 + 6 + 0 + 12 + 0 201+ 1 7 + 12 13 + 7 11+ 0 7 + 0 + 9 + 0 + 23 + 0 52 + 0 + 42 + 0 20 = a + a b 7a b + 12a b 13a b + 7ab b6 5 4 2 3 3 2 45 6 = a14 7a12 + 9a10 + 23a 8 52a 6 + 42a 4 20a 2 50. 8. m 7m + 9m 15 por m 5m + 9m 4m + 312 8416 12 847. x 9 4x 6 + 3x 3 2 por 3x 6 8x 3 + 10 1 7 + 9 15 1+ 0 + 0 4 + 0 + 0 + 3 + 0 + 0 2 1 5 + 9 4 + 3 3 + 0 + 0 8 + 0 + 0 + 10 1 7 + 9 153 + 0 + 0 12 + 0 + 0 + 9 + 0 + 0 6 5 + 35 45 + 75 8 + 0 + 0 + 32 + 0 + 0 24 + 0 + 0 + 16 + 9 63 + 81 135+ 10 + 0 + 0 40 + 0 + 0 + 30 + 0 + 0 20 4 + 28 36 + 603 + 0 + 0 20 + 0 + 0 + 51+ 0 + 0 70 + 0 + 0 + 46 + 0 + 0 20+ 3 21 + 27 45= 3x15 20x12 + 51x 9 70x 6 + 46x 3 201 12 + 53 127 + 187 192 + 87 45= m28 12m24 + 53m20 127m16 + 187m12 192m8 + 87m4 4510. 6a 4a + 6a 2 por a 2a + a 752429. x 5 3x 4 y 6x 3 y 2 4x 2 y 3 y 5 por 2x 2 + 4y 26+0+04+621 3 6 4 + 0 1 1+ 0 2 + 1 72+0+46+0+ 0 4+ 6 22 6 12 8 + 0 2 12 + 0 + 0 + 8 12 + 4+ 4 12 24 16 + 0 4 + 6+ 0 +04 +6 22 6 8 20 24 18 + 0 4 42 + 0 + 0 + 28 42 + 14= 2x 7 6x 6 y 8x 5 y 2 20 x 4 y 3 24 x 3 y 4 18x 2 y 5 4y 76 + 0 12 + 2 36 + 6 16 + 38 44 + 14 = 6a 9 12a 7 + 2a 6 36a 5 + 6a 4 16a 3 + 38a 2 44a + 1412. 3x 4 4x 3 y y 4 por x 3 5xy 2 + 3y 311. n 3n + 5n 8n + 4 por n 3n + 46 4 34 23 4 + 0 + 0 11+ 0 3 + 5 + 0 8 + 41+ 0 5 + 31+ 0 3 + 0 + 43 4 + 0 + 0 11+ 0 3 + 5 + 0 8 + 4 15 + 20 + 0 + 0 + 5 3 + 0 + 9 15 + 0 + 24 12+ 9 12 + 0 + 0 3 + 4 + 0 12 + 20 + 0 32 + 163 4 15 + 29 13 + 0 + 5 31+ 0 6 + 5 + 13 23 8 + 44 12 32 + 16= 3x 7 4 x 6 y 15x 5 y 2 + 29x 4 y 3 13x 3 y 4 + 5 xy 6 3y 7 = n10 6n8 + 5n7 + 13n6 23n5 8n 4 + 44n3 12n2 32n + 1613. x10 5x 6 y 4 + 3x 2 y 8 6y10 por x 6 4x 4 y 2 5x 2 y 4 + y 61+ 0 + 0 + 0 5 + 0 + 0 + 0 + 3 + 0 61+ 0 4 + 0 5 + 0 + 11+ 0 + 0 + 0 5 + 0 + 0 + 0 + 3 + 0 6 4 + 0 + 0 + 0 + 20 + 0 + 0 + 0 12 + 0 + 24 5 + 0 + 0 + 0 + 25 + 0 + 0 + 0 15 + 0 + 30 + 1 + 0+ 0 + 0 5 +0+ 0+0+ 3 +0 61+ 0 4 + 0 10 + 0 + 21+ 0 + 28 + 0 23 + 0 + 9 + 0 + 33 + 0 6x16 4 x14 y 2 10x12 y 4 + 21x10 y 6 + 28x 8 y 8 23x 6 y10 + 9x 4 y12 + 33x 2 y14 6y1615. a 5a 7apor 7a x + 3 + 6a x + 1 + a x x+2x +1x 1m1 m 314. a 3a + 5apor a 2 5 m1 3 + 0 + 5 1 5 + 0 71+ 0 5 7 + 0 + 6 +11 3 + 0 + 5 7 35 + 0 49 5 + 15 + 0 25 + 6 30 + 0 42 + 1 5+ 0 71 3 5 + 20 + 0 25 7 35 + 6 78 5 42 7 = a m + 2 3a m + 1 5a m + 20a m 1 25a m 3 = 7a 2 x + 5 35a 2 x + 4 + 6a 2 x + 3 78a 2 x + 2 5a 2 x + 1 42a 2 x 7a 2 x 1 51. 16. x 5x a 6 x a 2 por 6x a + 1 4 x a + 2x a 1 + x a 2a+217. a2x + 2 3a 2 x + 1 a 2 x 5a 2 x 1 por 6a 3x + 1 5a 3x + 3a 3x 1 1+ 0 5 + 0 61 3 1 5 6 4 + 2 +165+36 + 0 30 + 0 366 18 6 30 4 + 0 + 20 + 0 + 24 5 + 15 + 5 + 25 + 2 + 0 10 + 0 12 + 3 9 3 15+ 1+ 0 5 + 0 6 6 23 + 12 34 + 22 156 4 28 + 21 46 + 19 12 6= 6a 5x + 3 23a 5 x + 2 + 12a 5 x +1 34a 5 x + 22a 5 x 1 15a 5 x 2= 6x 2a + 3 4 x 2a + 2 28x 2a + 1 + 21x 2a 46x 2a 1 + 19x 2a 2 12x 2a 3 6x 2a 4EJERCICIO 46 ()( 4. x + 1 x 1 x + 1 2 2 2)( )( )( 6. a b a 2ab + b a + b 2 2)() (1. 4 a + 5 a 3 )( )x +12a 2 2ab + b 2 4a + 20 x2 + 1 a+ba3 x4 + x2a 3 2a 2b + ab2 4a 2 + 20a + x2 + 1+ a 2b 2ab2 + b3 12a 60 x 4 + 2 x2 + 1 a 3 a 2b ab 2 + b 3 4a 2 + 8a 60ab x2 1a 4 a 3b a 2b 2 + ab 3 x 6 + 2 x 4 + x2 (2. 3a x + 1 x 1 2)() x4 2 x 2 1 a 3b + a 2b 2 + ab3 b 4 3a 2 x + 3a 2a 4 2a 3b+ 2ab3 b 4 x6 + x4 x2 1 x1 3a 2 x 2 + 3a 2 x 3a 2 x 3a 2 3a 2 x 2 3a 2( )( 5. m m 4 m 6 3m + 2 )( ) ( )( 7. 3x x 2 2 x + 1 x 1 x + 1 )( ) m 4m 23x 6 x + 3x32 m 6x1 ( )(3. 2 a 3 a 1 a + 4 )( )m 3 4 m23x 4 6 x 3 + 3x 2 2a 6 6m2 + 24m 3 x 3 + 6 x 2 3x a 1 m 10m + 24m 323x 4 9 x 3 + 9 x 2 3x 2a 2 6a 3m + 2 2a + 6x+1 3m4 30m3 + 72m2 2a 2 8a + 63x 5 9 x 4 + 9 x 3 3x 2 + 2m3 20m2 + 48m a+4+ 3x 4 9 x 3 + 9 x 2 3 x 3m4 28m3 + 52m2 + 48m 2a 3 8a 2 + 6a 3x 5 6 x 4 + 6 x 2 3x + 8a 32a + 242 2a3 26a + 24 52. 11. (x 3)(x + 4)( x 5)( x + 1)()(8. x x + 1 x + x 1 x 22 2)( ) x3 x5x2 x + 1 x+ 4x+1x2 + x 1 x 2 3x x 2 5x + 4 x 12 + x 5x4 x3 + x2 x 2 + x 12 x2 4 x 5+ x3 x2 + x x2 4x 5 x2 + x 1 x 4 + x 3 12 x 2x4 x2 + 2x 1 4 x 3 4 x 2 + 48xx 2 5x 2 5x + 60x 5 x + 2x x32 x 4 3x 3 21x 2 + 43x + 60 2x 4+ 2x 4x + 2212. (x 3)( x + 2 x + 1)( x 1)(x + 3) 222x 2 x x + 4 x 2 5x + 2543x + 2x + 1 2 x2 3 x2 + 3x1 x + 2x + x 4 3 2 x 3 3x9. (a 3)(a + 2)(a 1)m m 1 m 1 + 3x 2 + 6 x + 3 x2+3 a 3 m x 4 + 2 x3 + 4 x2 + 6x + 3 x 3 x 2 3x + 3 a m 1 + 2x 3 x 2 3x + 3 2 m 1m 1+a 3a x 7 + 2 x 6 + 4 x 5 + 6 x 4 + 3x 3 2a m6 x 6 2 x 5 4 x 4 6 x 3 3x 2 2 m 1m 12a + am 3a6 3x 5 6 x 4 12 x 3 18 x 2 9 x a m 1 1+ 3x 4 + 6 x 3 + 12 x 2 + 18 x + 92 m 13m 22m2m 12a +a 3a 6ax +x x 7 6 5 x 4 9 x 3 9 x2 + 9 x + 92 m 1m 1 a + 3a 2a + 6 m13. 9a (3a 2)(2a + 1)(a 1)(2a 1)22 m 13m 22m2m 1a+a 3a 3a 2a m + 627a 3 18a 2 2a 1 a 3m 2 + a 2 m 1 3a 2 m 2 2a m 3a m 1 + 62a + 1a1 54a 4 36a 32a 2 a + 27a 18a 32 2a + 1(10. a a 1 a 2 a 3)()( )54a 9a 18a 4 32 2a 3a + 1 2a2 a 2a 2 3a + 1a2 108a 6 18a 5 36a 4a3 a2 162a 5 + 27a 4 + 54a 3 2a + 2a2 + 54a 4 9a 3 18a 2a 3a + 2a32 108a 180a + 45a 4 45a 3 18a 2 6 5a3a 4 3a 3 + 2a 2 x +114. a a + b x (x +2)(a x +1 b x + 2 )b x 2 x +1x+2 a +a bx 3a 3 + 9a 2 6a x +1 x a b b2 x + 2a 4 6a 3 + 11a 2 6a a 3 x + 2b x + a 2 x + 1b 2 x + 2 a 2 x + 1b2 x + 2 a xb 3x + 4 a 3 x + 2b x a xb 3 x + 4 53. EJERCICIO 47() 2 (11. 3 x + y 4 x y + 3x 2 3 y 2 ) 21. 4 ( x + 3) + 5( x + 2)= 3( x + y )( x + y ) 4 ( x y )( x y ) + 3x 2 3 y 2= 4 x + 12 + 5x + 10 = 3( x 2 + xy + xy + y 2 ) 4( x 2 xy xy + y 2 ) + 3x 2 3 y 2= 9 x + 22 = 3( x 2 + 2 xy + y 2 ) 4( x 2 2 xy + y 2 ) + 3x 2 3 y 2 () (2. 6 x + 4 3 x + 1 + 5 x + 22 2 2) ( )= 3x 2 + 6 xy + 3 y 2 4 x 2 + 8 xy 4 y 2 + 3x 2 3 y 2 = 6x + 24 3x 3 + 5x + 102 2 2 = 2 x 2 + 14 xy 4 y 2 = 8x + 31212. (m + n) (2m + n) + (m 4n)22 23. a (a x ) + 3a( x + 2a ) a( x 3a ) = a 2 ax + 3ax + 6a 2 ax + 3a 2= (m + n )(m + n ) (2m + n)(2m + n) + (m 4n)(m 4n) = 10a + ax 2= m2 + 2mn + n 2 (4m2 + 4mn + n 2 ) + m2 8mn + 16n 24. x ( y + 1) + y ( x + 1) 3x y2 22 2 2 2= 2m2 6mn + 17n 2 4m2 4mn n 2= 2m2 10mn + 16n 2 = x 2 y 2 + x 2 + x 2 y 2 + y 2 3x 2 y 2 = x2 y2 + x2 + y2() () ( )(13. x a + x + 3x a + 1 x + 1 a + 2 x a x) ()25. 4m 5mn + 3m (m + n ) 3m(m n ) + 3ax + 3x (ax + 2 x + a + 2 x ) (a x)(a x )3 2 2 2 2 2 2 = ax + x 22 = 4m3 5mn 2 + 3m4 + 3m2 n 2 3m3 + 3mn2 = 4ax + x + 3x ax 2 x 22 a 2 x (a ax ax + x )2 2= 3m4 + m3 + 3m2 n 2 2mn2 = 3ax x 2 + x a a 2 + ax + ax x 22 3 3 2 2 2(6. y + x y y x + 1 + y x + 1 y x 12 2 2) ( ) ( )= 2 x 2 + x + 5ax a a 2= y2 + x2 y3 x2 y3 y3 + x2 y2 + y2 x2 y2 + y2= y 3 + 3y214. (a + b c) + (a b + c) (a + b + c) 22 2( ) ( )( )7. 5 x + 2 x + 1 x + 4 6 x a+b cab+ c= 5x + 10 ( x + 4 x + x + 4) 6 x2a+ b c ab+ c a 2 + ab ac a 2 ab + ac= x + 10 x 2 4 x x 4+ ab + b 2 bc ab + b 2 bc= x 2 6x + 6 ac bc + c 2 + ac bc + c 28. (a + 5)(a 5) 3(a + 2)(a 2) + 5(a + 4) a + 2ab 2ac + b 2bc + c222 a 2ab + 2ac + b 2 2bc + c 22= a 2 5a + 5a 25 3(a 2 2a + 2a 4) + 5a + 20 a+b+ c= a 2 + 5a 5 3 (a 2 4) a+b+ c= a 2 + 5a 5 3a 2 + 12 a 2 + ab + ac= 2a 2 + 5a + 7 + ab + b 2 + bc9. (a + b)(4a 3b) (5a 2b)(3a + b) (a + b)(3a 6b) + ac+ bc + c 2= 4a 2 + ab 3b 2 (15a 2 ab 2b 2 ) (3a 2 3ab 6b 2 ) a + 2ab + 2ac + b + 2bc + c 222= 4a 2 + ab 3b 2 15a 2 + ab + 2b 2 3a 2 + 3ab + 6b 2a 2 + 2ab 2ac + b 2 2bc + c 2= 14a 2 + 5ab + 5b 2a 2 2ab + 2ac + b 2 2bc + c 2( ) ( )10. a + c a c2 2 a 2 2ab 2ac b 2 2bc c 2= (a + c)(a + c) (a c)(a c)a 2 2ab 2ac + b 2 6bc + c 2= a + ac + ac + c (a ac ac + c )2 2 2 2 a 2 + b 2 + c 2 2ab 2ac 6bc= a 2 + 2ac + c 2 a 2 + ac + ac c 2= 4ac 54. ( ) ( 215. x + x 3 x 2 + x + x x 3 2 2 2) (2)2( ) (2 16. x + y + z x + y x y + 3 x + xy + y2 2)( ) ( ) x + x 3 2 x + x22 x+ y+ z x+ yx+ y+ z x y x + x 3 2 x2 + x 2x 2 + xy + xz x 2 + xy x 4 + x 3 3x 2 x4 + x3 2x2+ xy+ y 2 + yz xy y 2 + x 3 + x 2 3x + x3 + x2 2x 3 x 2 3x + 9 2x2 2x + 4 + xz + yz + z 2 x2 y2 x 4 + 2 x 3 5x 2 6 x + 9 x 4 + 2 x 3 3x 2 4 x + 4x + 2 xy + 2 xz + y + 2 yz + z2 2 2 x2 x 3 x 2 + 2 xy + 2 xz + y 2 + 2 yz + z 2 x2 x 3 x2+ y23x + 3xy2+ 3y 2 x 4 x 3 3x 2 x 4 + 2 x 3 5x 2 6 x + 9 x 3 + x 2 + 3x x 4 2 x 3 + 3x 2 + 4 x 43x 2 + 5xy + 2 xz + 5y 2 + 2 yz + z 2 3x 2 + 3x + 9x 4 2 x 3 5x 2 + 6 x + 9 3x 2 + 5y 2 + z 2 + 5xy + 2 xz + 2 yz x 4 2 x 3 5x 2 + 6 x + 9x 4 2 x 3 7 x 2 + 4 x + 14[18. 3 ( x + 2) 4 ( x + 1) 3( x + 4) 2 ( x + 2)][ ][ ][17. x + (2 x 3) 3x ( x + 1) + 4 x x2] [][= 3x + 6 4 x 4 3x + 12 2 x 4 ] [][] = x + 2 x 3 3x x 1 + 4 x x 2 = [ x + 2][x + 8] = [3x 3][2 x 1] + 4 x x2= x 2 8 x + 2 x + 16 = 6 x 2 3x 6 x + 3 + 4 x x 2 = x 2 6 x + 16 = 5x 5x + 3220. [(x + y) 3(x y) ][(x + y)(x y) + x (y x)]2 2[()( )][ ( ) ( )] ) (19. m + n m n m + n m + n 2 m + n 3 m n)([ ][= x 2 + 2 xy + y 2 3 (x 2 2 xy + y 2 ) x 2 y 2 + xy x 2 ] = [m n (m + 2mn + n )][2m + 2n 3m + 3n][ ][xy y ] 2 2 22= x + 2 xy + y 3x + 6xy 3 y2 2 2 22 = [m n m 2mn n ][ m + 5n][ ][] 2 2 22= 2 x 2 + 8xy 2 y 2 xy y 2 = [ 2mn 2n ][ m + 5n] 2= 2 x 3 y + 2 x 2 y 2 + 8 x 2 y 2 8xy 3 2 xy 3 + 2 y 4 = 2m2 n 10mn2 + 2mn 2 10n 3= 2 x 3 y + 10x 2 y 2 10xy 3 + 2 y 4 = 2m n 8mn 10n22 3EJERCICIO 48[ 3. 3x 2 y + ( x 2 y) 2 ( x + y) 3(2 x + 1)][= 3x 2 y + x 2 y 2 x 2 y 6 x 3 ] [1. x 3a + 2 ( x + 1)][= 4x 6y 3 ] [ = x 3a 2 x + 2]= 4x + 6y + 3 = x 3a + 2 x 2 = 3 x 3a 2{ 4. 4 x 2 3x + 5 x + x 2 x[)] } (= 4x2 { 3x + 5 [ x + 2 x x ] }[ ]22. (a + b) 3 2a + b ( a + 2)[ = a b 3 2a ab + 2b ] = 4x2 { 3x + 5 + x 2 x + x } 2 = a b 6a + 3ab 6b= 4x2 { 4 x + 5 + x }2 = 7a 7b + 3ab 7a + 3ab 7b= 4x2 + 4x 5 x2= 3x 2 + 4 x 5 55. {[5. 2a 3x + 2 a + 3x 2 a + b 2 + a ()) ] }( [{(10. m 3(m + n) + 2m + n 2 3[m n + 1] + m) }] = m 3m 3n + [ { ( 2m + n 2 3m + 3n 3) + m}] = 2a { 3x + 2 [ a + 3x 2 ( a + b 2 a )] } = 2m 3n + [ { ( 5m + 4n 5) + m}] = 2a { 3x + 2 [ a + 3x + 2a 2b + 4 + 2a ] } = 2m 3n + [ {5m 4n + 5 + m}] = 2a { 3x + 2 [3a + 3x 2b + 4 ] } = 2m 3n + [ {6m 4n + 5}] = 2a { 3x + 6a + 6 x 4b + 8} [ = 2m 3n + 6m + 4n 5] = 2a + 3x 6a 6 x + 4b 8 = 2m 3n 6m + 4n 5 = 4a 3x + 4b 8 4a + 4b 3x 8 = 8m + n 5[6. a ( x + y ) 3 ( x y) + 2 ( x 2 y) 2 ( x y)][ = a x y 3x + 3 y + 2 x + 2 y + 2 x + 2 y] = a 4x + 2y + 2 x + 4y [] { [11. 3( x 2 y ) + 2 4 2 x 3( x + y) ] } { [ (x + y)] } = a 4x + 2 y + 2x + 8y= 3x + 6 y + 2 { 4 [ 2 x 3x 3 y ] } { [ x y] } = a 2 x + 10 y= 3x + 6 y + 2 { 4[ 5x 3 y] } {x + y} = 3x + 6 y + 2 {20 x + 12 y} x y{ [7. m (m + n) 3 2m + 2m + n + 2 ( 1 + n) (m + n 1) ]} = 4 x + 5 y + 40 x + 24 y{ [ = m m n 3 2m + 2m + n 2 + 2n m n + 1]}= 36 x + 29 y {[ = n 3 2m + 3m + 2n 1 ]} = n 3 { 2m 3m + 2n 1} = n 3 { 5m + 2n 1} = n + 15m 6n + 3{[12. 5 (a + b) 3 2a + 3b (a + b) + ( a b) + 2 ( a + b) a] } = 7n + 15m + 3 15m 7n + 3{[] }= 5 a b 3 2a + 3b a b a b 2a + 2b a{[] }= 5 a b 3 6a + 3b a{[8. 2 (a b) 3(a + 2b) 4 a 2b + 2 a + b 1 + 2 (a b)]} = 5 { 2 a b + 18a 9b} = 2a + 2b 3a 6b 4 {a 2b + 2 [ a + b 1 + 2a 2b] }= 5{16a 10b} = 5a 4b 4 {a 2b + 2 [a b 1] }= 80a 50b = 5a 4b 4 {a 2b + 2a 2b 2} = 5a 4b 4 {3a 4b 2} = 5a 4b 12a + 16b + 8{[13. 3 + ( a + b) ] } 4 { [ ( a b)] }= 3{ [ a + b] } 4 { [a + b] } = 17a + 12b + 8= 3{a b} 4 { a b}[ { }]9. 5 ( x + y) 2 x y + 2 x + y 3 ( x y 1) + 2 x= 3a + 3b + 4a + 4b = 5x 5y [2 x y + 2{ x + y 3 x + y + 1}] + 2 x= a + 7b = 3x 5y [2 x y + 2 { 2 x + 2 y 2}] [ = 3x 5y 2 x y 4 x + 4 y 4 ] { {[]} [14. a + b 2 (a b ) + 3 2a + b 3 (a + b 1) 3 a + 2 ( 1 + a ) ]} = 3x 5y [ 2 x + 3 y 4]= {a + b 2 a + 2b + 3 { [2a + b 3a 3b + 3] } 3[ a 2 + 2a ] } = 3x 5y + 2 x 3 y + 4 = x 8y + 4 = { a + 3b + 3 {a + 2b 3} 3a + 6}= { 4a + 3b + 6 + 3a + 6b 9}= { a + 9b 3}= a 9b + 3 56. EJERCICIO 491 8 9 4 4112. a b c 8c = = a 8b9 8 9 44a b c8 81. 24 8 = 3 16 6 4 3162. 63 7 = 9 13. 16m n 5n = 6 43mn= m6n5 53. 5a 2 a = 5a 2 1 = 5a 108 7 6 6 8 8 27 714. 108a b c 20b c ==7 6 8 6 8 ab c a4. 14a 3b 4 2ab 2 = 7a 3 1b4 2 = 7a 2b 22055. a 3b 4 c a 3b 4 = a 3 3b 4 4 c = c 2 2 1 6 6 215. 2m n 3mn =m n = m2 6 66. a b ab = a 2 1 1 133 2b=a16. a x a 2 = a x 27. 54x y z 6xy z = 9x2 1y 2 2z3 3 = 9x 2 2 32 317. 3a xbm ab 2 = 3a x 1bm 28. 5m2n m2n = 5m2 2n1 1 = 55 m 3 n 4 1 1 59. 8a 2 x 3 8a 2 x 3 = a 2 2 x 3 3 = 118. 5a b c 6a b c = m n3 4a b c = a m 3bn 466 xy 2 1xy10. xy 2y = =21 xm mn19. a b 4a b = x mm n 2 2 a b 45 4 4 5 1 511. 5x y 6x y = x y = y44 54 ax x2 333 320. 3m n x 5m n x = m n xa x 3x 2 3 = m a xnx 2665 5EJERCICIO 502. 2x a + 4 x a + 2 = 2x a + 4 b+ 2 g= 2x a + 4 a 2 = 2x 2 a1. am + 3 am + 2 = a m+3 m+2 b g= am + 3 m 2 = a 1 2n + 3 b+ 4g 11 2n + 3 4xn + 4 = = x 2n + 3 n 4 = xn 1 n4. xx3 m 2 b 5 g 3 m 2 m + 5 3 3444m 23. 3a 5am 5 = = a= ama5 55 m + 3 m 1 7 m + 3 4 m 1 2 7 m 1 m 36. 7x y 8x 4 y 2 =xy= x y x2 n 4 x 2 3 n 2 4 x 5 n 2 885. 4a b 5a b =b = a b3 2 a 55n 1 n +1 n 1 n +1 4 n 1 n + 1 n + 1 n 148. 4x y 5x y = x y =5 5557. 5a2m 1 x 3 b 6a 2m 2 b x4 = a 2m 1 2m + 2 b x 3 x + 4 = ab6 6 5 1 m 2 n 3 x10. 5ab c 6a b c = 2 3m n x a b c9. am + nb x + a amba = am + n mb x + a a = anb x6EJERCICIO 511 1 2 2 2 2 3 2 2 x = x = x1. 23 2 4 5. 2 x 4 y 5 2 = 9 x 4 y 5 = 2 x 4 y 5 = 1 x 4 y 539 2 1891 33 6. 3m4n5p 6 m4np 5 = 1 m4 4n5 1p 6 5 = 9n4p 3 3 3 4 2 15 3 a b a b = 5 a 3 2b1 1 =a= a32. 5 5420 4757 2 5 6 5 5 68 2 1 5 5 6 6 = 14 a = 7 a27. 8 a b c 2 ab c = 5 a b c 40 20 2 5 3 1 3 12 5 2 xy z z = 3 xy 5 z 3 3 = xy = 4xy 53. 3 61 36 22 x m 3 2 10 x 1 m 27 8. a b ab = 3 a x 1bm 2 = a b3 5 39 7 m n328 m 1 n 2 7 m 1 n 2 a b ab 2 = 8 a m 1b n 2 =a b = a b 54. 84 324 64 57. 311. 2a x + 4bm 3 1 a 4b 3 = 2 a x + 4 4bm 3 3 = 4a xbm 63 3 5 3 x21 c d d =8 c 3 d 5 x = 12 c 3 d 5 x = 1 c 3 d 5 x9. 8 4 3 2422 4 1312. a x 3bm + 5 c 2 a x 4bm 13 1553 m n 3 6 m n 3 1 1a b b 3 = 4 a m b n 3 = a b = a mb n 310. 4 2 312251= 15 a x 3 x + 4b m+ 5 m + 1c 2 = ab 6 c 2 = ab 6 c 22345 9 5EJERCICIO 52a x + am 1 a x am 1a 2 ab a 2 ab 10. = 2 + 2 = a x 2 + am 31. a ab a = = =a b2a2 aaa a am+211. 2a 3am+ 6am + 42. 3x y 5a x 3x 2 32 4 2 3x 2 y 3 5a 2 x 4 3x 2 y 3 5a 2 x 45 2 2 3a 3 = == y3 + a x 3x 2 3x 2 3x 23 2am 3am + 2 6am + 4 2= += am 3 + am 1 2am + 1 3a 3 3a 3 3a 333. 3a 5ab 6a b 32 2 3m 1 n + 2 m2 n+4 2a 12. a b + a b a b m n 2 33a35ab 6a b2 3 5 2 3 ab = = a 2 + b 2 + 3ab 3 2a 2a 2a2 2ambn am 1bn + 2 am 2bn + 4= 2 3 +ab a 2b 3a 2b 3 x 3 4x 2 + x x 3 4x 2 x4. = + = x 2 4x + 1= a b + a b a m 4 bn + 1 m2 n3m 3 n1xx x xm+213. x 5 x m + 6 xm + 1 x m 15. 4x 10x 5x 8 64xm 2 2x 3 m+2x 5x m 6x m + 1 x m 14x 8 10x 6 5x 45= m2 m 2 + m 2 m2 = 3 = 2x 5 5x 3 x x x x x2x 2x 32x 32= x 4 5x 2 + 6x 3 x x 4 + 6 x 3 5 x 2 x6. 6m 8m n + 20mn 3 22x + 4 m1 2m 14. 4a b 6a x + 3 b m 2 + 8a x + 2 b m 36m3 8m2n 20mn2 2a x + 2 b m 4 = += 3m2 + 4mn 10n2 2m 2m 2m 4a x + 4 b m 16a x + 3 b m 28a x + 2 b m 3=x+2 m4x+2 m4+ 2a b 2a b 2a x + 2b m 47. 6a b 3a b a b 8 86 6 2 3 2 3= 2a 2b 3 + 3ab 2 4b 3a b6a 8b 8 3a 6b6 a 2b 3 1 = 2 3 = 2a 6b 5 a 4b3 EJERCICIO 533a b3a 2b3 3a 2b3 38. x 5x 10x + 15x43 2 1 2 2 5x xx36 31. 2 3 = x = x 1x4 5x 3 10x 2 15x12 2 46 4 = + = x 3 + x 2 + 2x 3x x 5x 5 x 5x 5 x53 39. 8m n 10m n 20m n + 12m n9 2 7 45 63 81 3 3 2 1a aa 2m 23 5+ 43 33 8m9n2 10m7n4 20m5n6 12m3n8 = + 2.5 552m2 2m22m2 2m2 5 3 15 2 5 55 = 4m n 5m n 10m n + 6mn 7 2 5 4 3 68= a +a a = a 3