Upload
others
View
8
Download
0
Embed Size (px)
Citation preview
18
2
(18 )
2.1 (1 )
2.2 (2 )
2.3 (2 )
2.4 (4 )
2.5 (4 )
2.6 (5 )
1.
2.
19
2.1
1.
2.
2.1
1. x y
2. 2.1
3.
-5 x -5 x -5
-5x0 x 1 x
1
2.2
1.
2.
2.2 2.2 2.2
1.
1, 2 3
-3 5
21
0.75
2x 3x
19
20
-5a2
2a2
7pq 0.2pq
-2x2y 3yx
2
–
2.
–
3x4 + 2x
4 = (3 + 2)x
4
= 5 x4
2.2
3.
2.2
4. 2.2
2.3
1.
2.
1.
1) 5a -2a
2) 2x 3y
3)
(1) x2 + 3x
2y
(2) 3x2y – 2xy
(3) xy + yz – zx
(4) x2y
2 + 7z
2y
2
(5) x2 + y
2 + z
2
20
21
2.
x
y
2x + 2y
3.
2.4
1.
2.
1. – 4 – 5
2.
1) -5 5
2) -5 (-1)(5)
3) -x x
4) -x (-1)(x)
5) -(x+2 ) x+2
6) -(x +2) (-1)(x+2)
-(x + 2) = (-1)(x + 2)
= (-1)(x) + (-1)(2) ( )
= (-x) + (-2)
y
x
y
x
21
22
x + 2 (-x) + (-2)
-(x + 2) x + 2
x + 2 (-x) + (-2)
-x x
-2 2
x – 2 x – 2
x – 2 x + (-2) x + (-2)
- [x+ (-2)] = (- x) + 2
-x x 2 -2
3. x2 – 7xy – 6
x2 – 7xy – 6 = -(x
2 – 7xy – 6)
-(x2 – 7xy – 6) = -[x
2 + (-7xy) + (-6)]
-(x2 – 7xy – 6) = -x
2 + 7xy + 6
4.
1) 6x2 – (2x
2 – x) = 6x
2 – 2x
2 + x
= 4x2 – x
2) (4x3 – 5x
2) – (3x
3 + x
2 – 1) = 4x
3 – 5x
2 – 3x
3 – x
2 + 1
= x3 – 6x
2 + 1
5.
6.
22
23
+ =
7. 2.4 3 5) 6)
3) 5) 2) 6)
8.
9. “ ”
2.5
2.5 2.5
1.
2.
4
3. “ ”
1)
(2x3 + 4x) + (5x
2 – 2x
3) = 5x
2 + 4x
-2x4 + (2x
4 – 5) = -5
2)
(1)
(-2) (3x2 – 5) = -6x
2 + 10
23
24
(2)
4x(3x2 – x + 1) = 12x
3 – 4x
2 + 4x
4. “ ”
2.5
5. 2.5
2.6
2.6
1.
2.
5
43 = 54
53
7
2 6 = 72
76
x
3xx 2
= x
3x x
x 2
3x
xx 23
= 3xx
3xx 23
3. ( )
4.
=
24
25
5. “ ”
6. 2.6
2.1
1.
1) -1, 0 2) 1, 0
3) 1, 1 4) -0.17, 0
5)38
, 4 6) -5, 1
7) -31
, 1 8) 2, 3
9) -1, 3 10) 9, 9
11) -51
, 5 12) 1, 4
13) -1, 2 14) -1, 4
15)6
13, 7 16) -4 , 6
17)37
, 2 18) -81
, 3
2. 2x, 2-1x
2 5x
3
3. -3x2y
2, -3x
3y -3xy
3
38
8xy2, - 45
16 xy2 51xy
2
-12x2y 3
2 x2y
34 xy -xy
25
26
2.2
1.
1) 2)
3) 4)
5) 6)
7) 8)
9) 10)
2.
1) -5x 2) 18y
3) 6x + 6y 4) 23
5) 5x2
6) 3yz
7) 2x2y + xy
2 8) 4y
5
9) -7x4y – 7xy
410) -tx
3
3.
1) 13x 2) -2y
3) 6x – 6y 4) -47
5) x2
6) 7yz
7) 2x2y – xy
2 8) 0
9) -7x4y + 7xy
410) -7tx
3
4.
1) 3x 2) -23y
3) 6x 4) -18y
5) 6u 6) 3w2
7) 12r2s 8) 0
9) 2x2– 3y
2 + 6z
3 10) 9st + 4s
2t2
5.
1) 0 2) 4y
3) 5z 4) 13y2
5) x2
6) 0
7) -17s3
8) 0
9) 6xy 10) 8xy2
11) -yz 12) -29s2 t
26
27
48
1) 0 2) 0
3) 1 4) 1
5) 2 6) 1
7) 2 8) 2
2.3
1.
1) 2x – 10
2) 3z2
3) 3x3 – 2x
2
4) 2x – xy + 4
5) 3x2y + y
2 + 6
2.
1) 1
2) 2
3) 3
4) 2
5) 3
3.
1) 8x + 3
2) -3y2 + 6y
3) -13z3 – 10z
2
4) -5z3 – 4z
2 – 5z
5) x2 – 7x – 2
4.
1) 3 + 2x
2) 5 – 3x + x2
3) -5 + 6x – 2x2
5) 4 + 7x – x3
6) 1 – x + 8x2 + 4x
3
27
28
2.4
1.
1) -7x + 15 2) x – 14
3) -9x + 5y + 4 4) 7z2 + 3z – 10
5) 6x2 + 12 x – 1 6) -6s + 2st
7) 10xy – 11st 8) x2 – 2x – 1
9) - r + 9s – 9t 10) 3x + 17y – z – 13
11) y2 – 3y + 2 12) 4r – 2x – y
2.
1) 2x – 2y 2) 11x + 4y + 17
3) 3x + y – 8 4) 18z2 + 10z + 1
5) -7x2 –3x + 8 6) 2x
2 + 5x – 11
7) -7x2 + x + 8 8) 2x
2 – 2x – 9
9) 3x – 4 10) -6r + 6s + 6t
11) 21x – 9 12) -3x2 – 16x – 17
2.4
1.
1) 2x – 7 2) -20x + 11
3) 0 4) -7x2 + 14x + 3
5) -2x2 –2x – 10 6) 9x
2 – 18x – 10
2.
1) -7xy + 3x + y – 23xy – 3x + 3y
2) 4z2 + 16z – 4 4z
2 – 2z – 6
3) -2x – 21 2x2 – 10x + 21
4) 6r + 16s – 10t -6r + 10s – 6t
5) 8x2 – 6x – 5 2x
2 + 18x – 3
6) 23
x2 –
35
x + 12 21
x2 +
31
x – 8
28
29
3.
1) 9x2 – 8x – 20 2) -x
2 – 12x – 6
3) -5x2 + 10x + 4 4) -15x
2 + 6x +18
5) -13x2 + 7x + 10 6) 3x
2 + 13x – 2
2.5
1.
1) 6x2
2) xy
3) 27xy 4) 4x3
5) 2xy2
6) 0
7) 52x2y 8) -99x
2y
3
9) -12x4y 10) -60x
3y
3
11) -28y3z
2 12) -56y
4z
4
2.
1) 30x + 12 2) 2x + 3
3) x2 – x 4) 56x
2 – 63x
5) 20x2+ 18x 6) -4x
2 + 24x
7) -5x3 – 40x 8) 6x
2 – 8x –14
9) 9x3 + 18x
2 – 27x 10) 7x
4 – 10x
3
11) -6x4 + 3x
2 – 18x 12) -48x
4 + 40x
3 – 88x
2
1.
2.
29
30
2.6
1) -2x 2) 5x
3) 3x
4) 2
y2
5) 4y 6) 23
xy
7) -4x2
8) 3xy
9) 45
x2
10) -x2y
11) 6y2
12) 21
x2y
2.6
1.
1) 2x – 4 2) -2x + 5
3) 2x2 + 1 4) x
2 – 4
5) 3x2 – 5x 6) 3x + 8
7) 2x – 3 8) 3x – 7
9) 1 – 4x 10) -x2 – 6x + 1
2.
1) 45
– 4
3x 2) 2x
2 + 4
3) 5
4x–
51
4) 5 – 4x2
5) -3 – 7x2
6) 8x – 3
7) -3x + 4 8) -1 – 3x
9) 6x2 – 5x + 3 10) x
2 –
43x
– 2
3.
1) 4x2 – 4x 2) 3x
2 – 7x
3) 10x – 4x3
4) -18x3 –24x
2
5) -7x3 + 28x
2 6) -15x
3 + 5x
2 –30x
30
3131
32
x
x
2.1
1. AB AB
[x ]
2. CD 3 AB CD
[3x ]
3. x
[x2 ]
4. x
[x 3
]
5. x 4
[4 x2
]
A B
x
xx
x
x
32
33
6. x y
[xy ]
7. 6 4
[4xy ]
8. x y z
[xyz ]
y
x
x
y
yx
z
33
34
2.2
1.
( ) ( ) ( ) ( )
2 3 (2 2) + (2 3) = 10 2 3 = 6
3 5 (2 3) + (2 5) = 16 3 5 = 15
4 5 (2 4) + (2 5) = 18 4 5 = 20
7
x
10
y
(2 7) + (2 10) = 34
2x + 2y
7 10 = 70
x y = xy
2.
x y
2x + 2y xy
.
.
.
.
.
.
.
.
.
.
.
.
34
35
2.2
1. 5 + 3 [ 8 ]
2. 5.4a + 6.7a [ 12.1a ]
3. 7x + (-13)x [ -6x ]
4. -5x2 + 5x
2 [ 0 ]
5. x21 + x
31
[ x ]
6. 11.5ab + (-6.3ab) [ 5.2ab ]
7. [2xy + xy] + (-xy) [2xy ]
8. xy xy 21 +
41 xy [ xy ]
9. 3
m 3
+ 4m3 +
32m 3
[5m3]
10. -4m3 +
32m
3m 33
[-3m3]
11. xy + (-2xy) + (-3xy) [-4xy ]
12. [-12pqr + 7pqr] + (-5pqr) [ -10pqr ]
13. -12pqr + [ 7pqr + (-5pqr)] [ -10pqr ]
14. [-3x3 + 15x
3 ]+[ 3x
3 + (-12x
3)] [ 3x
3 ]
15. [-3x3 + 3x
3 ]+ [15x
3 + (-12x
3)] [ 3x
3 ]
5
6
_
7
4
_
35
36
2.2
1. 11 – 23 [ -12 ]
2. 2.8x – (-3x) [ 5.8x ]
3. -5x – 9x [ -14x ]
4. 2x2 – (- 4 x
2) – 2 x
2[ 4x
2 ]
5. 3x2y – 4 x
2y – 5 x
2y [ -6x
2y ]
6. -4m – 3m – (-7m) [0]
7. 7pq – (11pq – 9pq) [ 5pq ]
8. (7pq – 11pq) – 9pq [ -13pq ]
9. 24xy – 6xy – 14 xy [ 4xy ]
10. 3xyz – (7xyz – xyz) [-3xy ]
11. (3xyz –7xyz) – xyz [-5xy ]
12. (2ab – ab + ab) – (2ab – 2ab) [ 2ab ]
13. (2ab – ab)+ (ab –2ab – 2ab) [ -2ab ]
14. -5x2y – (-6x
2y) – 5x
2y – 6 x
2y [ -10x
2y ]
15. [-5x2y – (-6x
2y)] – [5x
2y + (-6 x
2y)] [ 2x
2y ]
36
37
2.5
1. 6 6 30
2. 6 2 50
3. 6 3 10
1. 3
5 1
2.
x
1 x
y x
1)
x2
x
xy
x
x
x x
1 y
37
38
2)
……… [x ]
……… [x + 3 ]
[x(x + 3)]
……… [x2 + 3x ]
3)
2x
(
)
……… [x - 2 ]
……… [x ]
………
[x(x - 2)]
..……
[x2 - 2x ]
4)
x
x 11 1
x
x
y
x – 2 1 1
x
x
38
39
……… [x ]
……… [x + y ]
[x(x + y)]
……… [x2 + xy ]
3. 2 – 3
39
40
2.5
1. 4 4
5 5 6 6 7 7
2. 1
1
2
………… …………[4 (4 – 2)] + 4 [4 (5 – 2)] + 4
12 16
(2 4) + 2(4 – 2) …………(2 5) + 2(5 – 2)
12 16
…………
40
41
3
3. n n
1
1 1 = (2 n) + 2 (n – 2)
= 2n + 2n – 4
= 4n – 4
= 4(n – 1)
2 1 = 4 (n – 2) + 4
= [(4 n) – (4 2)] + 4
= 4n – 8 + 4
= 4n – 4
= 4(n – 1)
3 1 = 4 (n – 1)
= 4(n – 1)
4.
4n – 4 4(n – 1)
5.
20 20
1
4 (5 – 1) ………… …………4 (4 – 1)
12 16
41
42
n2 – 4(n – 1) = 20
2 – (4 19)
= 400 – 76
= 324
324
42
4343
44
2.6
1.
1) 6a – 4a – 5a [-3a]
2) 5x2y + 6x
2y [11x
2y]
3) 7pq + 11pq – 9pq [9pq]
4) 24xy – 6xy – 8xy [10xy]
5) -3x2y
3 + 7x
2y
3 – 15x
2y
3[-11x
2y
3]
2.
1) 3x – 2 + x – 9 [4x – 11 1]
2) 2a + 5 –
4a – 3 [ + 2 1]
3) -5x3 – 2x
2 + 5x
3 – x [-2x
2 – x 2]
4) a3 + a
2 + 3 + a
3 + 2a – a
2[2a
3 + 2a + 3 3]
5) -18xy – 6x2y + 15xy [-6x
2y – 3xy 3]
3.
1) (2x + 5) + (3x – 7) [5x – 2]
2) (4x2 – 6) + (x
2 – 5x + 4) [5x
2 – 5x – 2]
3) (3x2 – 7) – (x + 5) [3x
2 – x – 12]
4) (4x2 – 5x) – (-3x
2 – 5) [7x
2 – 5x + 5]
5) (-5x2 + 8x – 1) – (-4x
2 – 2x + 3) [-x
2 + 10 x – 4]
4)
1) (-9x3)(2x
2) [-18x
5]
2) (7x3)(-x
2y) [-7x
5y]
3) (-10a2b
3)(-2ab) [20a
3b
4]
4) 8xy (-2xy) [-4]
5) (-15a2b
3) (-3ab
2) [5ab]
6) (-24mn2) (6mn) [-4n]
5.
1) (-5)(2x2 – 3) [-10x
2 + 15]
2) 7m (-2m2 + m + 1) [-14m
3 + 7m
2 + 7m]
3) (-2mn)(3m2 – n) [-6m
3n + 2mn
2]
4) (xy)(-1 + 2x – 3y) [-xy + 2x2y – 3xy
2]
5) x2(4x
2 – 3x – 5) [4x
4 – 3x
3 – 5x
2]
a
2
_
44
45
6.
1) (x2 – 2x) x [x – 2]
2) (10a3 + 4a
2 – a) (2a) [5a
2 + 2a – ]
3) (-9x2 – 12x + 4) (-3) [3x
2 + 4x – ]
4) (25x3 – 10x
2 – 15x) (5x) [5x
2 – 2x – 3]
5) (-14x2y – 7xy
2 + 21xy) (-7xy) [2x + y – 3]
7. a b [a – b ]
8. 2x, y x
[3x + y ]
9. ( x y
)
[x2 + 2xy ]
10. x y z
[xy + 2yz + 2xz ]
y
x y
y
y
x
z
yx
2
1_
3
4_
45