Objective - To recognize and factor a perfect square trinomial and difference of squares.

Find the area of the square in terms of x.

2x + 3

2 3A = s2

A (2 3)22x + 3

Perfect Square Trinomial

A = (2x + 3)2

A = (2x + 3)(2x + 3)A = 4x2 +12x + 9

Simplify.1)

2)

4)

5)

(x + 5)2

(m− 2)2

(2k − 5)2

(3t + 4)2

(x + 5)(x + 5)x2 +10x + 25

(m 2)(m 2)

(2k − 5)(2k − 5)4k2 − 20k + 25

(3t + 4)(3t + 4)

3) 6)(2x + 7)2 (11− y)2

(m− 2)(m− 2)m2 − 4m+ 4

(2x + 7)(2x + 7)4x2 + 28x + 49

(3t + 4)(3t + 4)9t2 + 24t +16

(11− y)(11− y)121− 22y + y2

Follow the pattern!(a + b)2 = a2 + 2ab + b2

(x + 5)2 = x2 +10x + 25(y− 3)2 = y2 − 6y + 9

LastTerm

Twicethe

Squareof theTerm the

LastTerm

of the Last

Term

Factor.m2 +12m + 36

y2 −14y + 49

=

=

(m+ 6)2

(y− 7)2

Factor.1)

2)

5)

6)

x2 − 4x + 4

y2 +10y + 25

4x2 −12x + 9

m2 +14m+ 28

2(x 2)−

2(y 5)+

2(2x 3)−

Not Factorable3)

4)

7)

8)

t 2 −18t + 81

y2 + 20y +100

t 2 − 8t +16

9k2 + 6k + 4

2(t 9)−

2(y 10)+

2(t 4)−

Not Factorable

Factor the perfect square trinomials.1)

2)

4)

5)

x2 −12x + 36

y2 −14y + 49

k2 − 22k +121

4x2 + 28x + 49

2(x 6)−

2( 7)

2(k 11)−

2(2 7)

3) 6)t 2 − 2t +1 9x2 −12x+16

2(y 7)−

2(t 1)−

2(2x 7)+

Not Factorable

Complete the perfect square trinomial and factor.

1)

2)

3)

x2 + 6x +

m2 +12m +

y2 18y +

9 2(x 3)= +

36 2(m 6)= +

81 2(y 9)3)

4)

5)

y −18y +

k2 −14k +

4t2 − 20t +

81 (y 9)= −

49 2(k 7)= −

25 2(2t 5)= −

Lesson 8-5

Algebra Slide Show: Teaching Made Easy As Pi, by James Wenk © 2010

Factoring Polynomials

2) Trinomial Factoring : 2x bx c+ +

Five Types of Factoring

1) Greatest Monomial Factor (Group) 1) Greatest Monomial Factor (Group)

2) Trinomial Factoring : 2x bx c+ +

3) Trinomial Factoring : 2ax bx c+ +

4) Perfect Square Trinomial

5) Difference of Squares

3) Trinomial Factoring : 2ax bx c+ +

4) Perfect Square Trinomial

Difference of Squares

Multiply.1)

2)

(x + 3)(x − 3)

(m+ 7)(m− 7)

2x 9= −2m 49= −

3)

4)

(y +10)(y−10)

(t + 8)(t − 8)

Inner and Outer terms cancel!

2y 100= −2t 64= −

Factor.1)

2)

3)

4)

x2 − 9

m2 − 49

y2 −100

t 2 64

(x 3)(x 3)= + −

(m 7)(m 7)= + −

(y 10)(y 10)= + −

(t 8)(t 8)4) t 2 − 64

5)

6)

7)

x2 − y2

16− k2

p2 −1

(t 8)(t 8)= + −

(x y)(x y)= + −

(4 k)(4 k)= + −

(p 1)(p 1)= + −

Difference of Squares?

a2 − 25Factor.

PerfectSquare

PerfectSquareminus

(a 5)(a 5)= + −

List the perfect squares from 1 to 200.149

16

25364964

81100121144

169196

Factor.1)

2)

5)

6)

x2 − 81

9m2 −121

t 2 − 50

4x2 − 49(x 9)(x 9)+ −

(3m 11)(3m 11)+ −

Not Factorable

(2x 7)(2x 7)+ −

3)

4)

7)

8)

16 − 49k2

k4 − 4

36y2 −1

16x2 + 25

(3m 11)(3m 11)+

(4 7k)(4 7k)+ −

2 2(k 2)(k 2)+ −

(2x 7)(2x 7)+

(6y 1)(6y 1)+ −

Not Factorable

Factoring Polynomials

2) Trinomial Factoring : 2x bx c+ +

Five Types of Factoring

1) Greatest Monomial Factor (Group) 1) Greatest Monomial Factor (Group)

2) Trinomial Factoring : 2x bx c+ +

3) Trinomial Factoring : 2ax bx c+ +

4) Perfect Square Trinomial

5) Difference of Squares

3) Trinomial Factoring : 2ax bx c+ +

4) Perfect Square Trinomial

5) Difference of Squares

Lesson 8-5 (cont.)

Algebra Slide Show: Teaching Made Easy As Pi, by James Wenk © 2010

Factor completely.1) 2x2 − 50

2(x2 − 25)

2(x + 5)(x − 5)

Greatest Monomial Factor

Difference of Squares

2) m4 −1

(m2 +1)(m2 −1)

(m2 +1)(m +1)(m−1) Difference of Squares

Difference of Squares

Factor completely.1) 3y2 − 27

4

3) 5m6 − 20

4

3(y2 − 9)

3(y + 3)(y − 3)

5(m6 − 4)

5(m3 + 2)(m3 − 2)

2) x4 − 81 4) 5y4 − 80

(x2 + 9)(x2 − 9)

(x2 + 9)(x + 3)(x − 3)

5(y4 −16)

5(y2 + 4)(y2 − 4)

5(y2 + 4)(y + 2)(y − 2)

Factor completely.1)

2)

5x2 + 30x + 455(x2 + 6x + 9)

5(x + 3)2

Greatest Monomial Factor

Perfect Square Trinomial

4 8 2 +162) x − 8x +16(x2 − 4)2

(x2 − 4)(x2 − 4)

Difference of Squares

Perfect Square Trinomial

(x + 2)(x − 2)(x + 2)2 (x − 2)2

(x + 2)(x − 2)

Factor completely.1)

2)

3x2 − 24x + 483(x2 − 8x +16)

3(x − 4)2

4 2 2 +12) x − 2x +1(x2 −1)2

(x2 −1)(x2 −1)

(x +1)(x −1)(x +1)2 (x −1)2

(x +1)(x −1)

Factor completely.1) 23x 30x 75+ +

23(x 10x 25)+ + Greatest Monomial Factor23(x 5)+ Perfect Square Trinomial

2) x4 − 5x2 + 4

Difference of Squares(x + 2)(x − 2)(x +1)(x −1)

Factoring(x2 − )(x2 − ) 1• 42 •241 x2 + bx + c

Factor completely.

1) x4 − x2 −12

Difference of Squares(x2 + 3)(x + 2)(x− 2)

Factoring(x2 + 3)(x2 − 4)1•122 •63• 4

x2 + bx + c

2) 4x4 −17x2 + 4

Difference of Squares(x + 2)(x− 2)(2x +1)(2x−1)

Factoring(1x2 − 4)(4x2 −1)1 4•2 2•

1 4•2 2•

14

41

161

ax2 + bx + c

Lesson 8-5 (cont.)

Algebra Slide Show: Teaching Made Easy As Pi, by James Wenk © 2010