10.7 Factoring Special Products

Difference of Two Squares Pattern/

Perfect Square Trinomials

Objectives

• I will identify and use special product patterns to factor quadratic polynomials.

Factoring the Difference of Two Squares

1. x2 - 36

= x2 - 62 Write in a2 - b2 form

= (x + 6)(x - 6) Factor using the pattern (a + b)(a - b) = a2 -

b2

Factoring the Difference of Two Squares

2. 9x2 - 121

= (3x)2 - 112 Write in a2 - b2 form

= (3x + 11)(3x - 11)Factor using the pattern (a + b)(a - b) = a2 - b2

Factoring the Difference of Two Squares

3. 12x2 - 75

= 3(4x2 - 25) Factor out a common factor

= 3[(2x)2 - 52] Write in a2 - b2 form

= 3(2x + 5)(2x - 5) Factor using the pattern(a + b)(a - b) = a2 - b2

Guided Practice

Factor

1. x2 - 169

2. 16x2 - 9

3. 20x2 - 20

(x + 13)(x - 13)

(4x + 3)(4x - 3)

5(2x + 2)(2x - 2)

Factoring Perfect Square Trinomials

4. x2 - 6x + 9

x2 - 2(x)(3) + 32 Write in a2 - 2ab + b2 form

(x - 3)2 Factor using pattern

Factoring Perfect Square Trinomials

5. 4x2 + 28x + 49

(2x)2 + 2(2x)(7) + 72 Write in a2 - 2ab + b2 form

(2x + 7)2 Factor using pattern

Guided Practice

Factor

1. x2 - 18x + 81

2. x2 + 24x + 144

3. 9x2 + 30x + 25

(x - 9)2

(x + 12)2

(3x + 5)2

Independent Practice

Factor

1. x2 - 25

2. x2 + 26x + 169

3. 4x2 - 81

(x + 5)(x - 5)

(x + 12)2

(2x + 9)(2x - 9)