Objective - To recognize and use the factoring pattern, Difference of Squares.

Multiply.1)

2)

3)

4)

(x 3)(x 3)

(m 7)(m 7)

(y 10)(y 10)

(t 8)(t 8)

2x 9 2m 49 2y 100

2t 64

Inner and Outer terms cancel!

Factor.1)

2)

3)

4)

2x 92m 49

2y 1002t 64

(x 3)(x 3)

(m 7)(m 7)

(y 10)(y 10)

(t 8)(t 8)

5)

6)

7)

2 2x y216 k

2p 1

(x y)(x y)

(4 k)(4 k)

(p 1)(p 1)

Factoring Polynomials

Five Types of Factoring

1) Greatest Monomial Factor

2) Difference of Squares

3) Perfect Square Trinomial

4) Trinomial Factoring : 2x bx c

5) Trinomial Factoring : 2ax bx c

1) Greatest Monomial Factor

2) Difference of Squares

Difference of Squares?

2a 25Factor.

(a 5)(a 5)

PerfectSquare

PerfectSquareminus

List the perfect squares from 1 to 200.149

16

25364964

81100121144

169196

Factor.1)

2)

3)

4)

5)

6)

7)

8)

2x 81

29m 121

216 49k

4k 4

2t 50

24x 49

236y 1

216x 25

(x 9)(x 9)

(3m 11)(3m 11)

(4 7k)(4 7k)

2 2(k 2)(k 2)

Not Factorable

(2x 7)(2x 7)

(6y 1)(6y 1)

Not Factorable

Factor completely.1)

2)

22x 5022(x 25)

2(x 5)(x 5)

Greatest Monomial Factor

Difference of Squares

4m 12 2(m 1)(m 1)

2(m 1)(m 1)(m 1) Difference of Squares

Difference of Squares

Factor completely.1)

2)

23y 27

4x 81

3)

4)

65m 20

45y 80

23(y 9)

3(y 3)(y 3)

2 2(x 9)(x 9) 2(x 9)(x 3)(x 3)

65(m 4)3 35(m 2)(m 2)

45(y 16)2 25(y 4)(y 4)

25(y 4)(y 2)(y 2)