1. Factoring Differences of Squares
Lesson 9-5
Factoring Differences of Squares

2. Factor a2 - b2 = (a - b)(a + b)
Both factors must be perfect squares.
Factor the binomial
x2 - 25
x = x2 - 52
= (x + 5)(x - 5)
Factor the binomial
36x2 - 49y2
36x2 - 49y2 = (6x)2 - (7y)2
= (6x + 7y)(6x - 7y)

3. Factor
x2 - 64
16y2 - 81z2

4. Factor out a Common Factor
48a3 - 12a
= 12a (4a2 - 1)
= 12a (2a + 1)(2a - 1)

5. Factor
3y3 - 27y

6. Apply factoring techniques more than once.
= 2[(x2)2 - 92]
= 2(x2 + 9) (x2 - 32)
= 2(x2 + 9) (x - 3)(x + 3)

7. Factor 4x

8. Apply Several Different Factoring Techniques.
5x3 + 15x2 - 5x - 15
= 5 (x3 + 3x2 - x - 3)
= 5 [(x3 - x)+(3x2 - 3)]
= 5 [x(x2 - 1)+3(x2 - 1)]
= 5 (x2 - 1)+(x + 3)
= 5((x + 1)(x - 1)(x + 3)

9. Factor
6x3 + 30x2 - 24x - 120

10. Solve by Factoring

11. Solve by Factoring
48x3 = 3x

12. Solve by Factoring
A square with side length x is cut from the right triangle shown below.
a. Write an equation in terms of x that represent the area of A the figure after the corner is removed. 16 x x
b. What value of x will result in a figure that is ¾ of the area of the original triangle? Show how you arrived at your answer. 8