1. Chapter 7
Factoring

2. The Difference of Squares
7.3 Special Factoring
The Difference of Squares
Difference of Squares
x2 – y2 = (x + y)(x – y)
Copyright © 2010 Pearson Education, Inc. All rights reserved.

3. Factoring Differences of Squares
7.3 Special Factoring
EXAMPLE 1
Factoring Differences of Squares
Factor each polynomial.
(a) 2n2 – 50
Copyright © 2010 Pearson Education, Inc. All rights reserved.

4. Factoring Differences of Squares
7.3 Special Factoring
EXAMPLE 1
Factoring Differences of Squares
Factor each polynomial.
(b) 9g2 – 16
(c) 4h2 – (w + 5)2
Copyright © 2010 Pearson Education, Inc. All rights reserved.

5. 7.3 Special Factoring Caution
Assuming no greatest common factor except 1, it is not possible to
factor (with real numbers) a sum of squares, such as x
Copyright © 2010 Pearson Education, Inc. All rights reserved.

6. Factoring Perfect Square Trinomials
7.3 Special Factoring
EXAMPLE 2
Factoring Perfect Square Trinomials
Factor each polynomial.
(a) 9g2 – 42g
Copyright © 2010 Pearson Education, Inc. All rights reserved.

7. Factoring Perfect Square Trinomials
7.3 Special Factoring
EXAMPLE 2
Factoring Perfect Square Trinomials
Factor each polynomial.
(b) 25x xy y2
Copyright © 2010 Pearson Education, Inc. All rights reserved.

8. Factoring Perfect Square Trinomials
7.3 Special Factoring
EXAMPLE 2
Factoring Perfect Square Trinomials
Factor each polynomial.
(d) c2 – 6c – h2

9. 7.3 Special Factoring Difference of Cubes
x3 – y3 = (x – y)(x2 + xy + y2)
Copyright © 2010 Pearson Education, Inc. All rights reserved.

10. 7.3 Special Factoring Sum of Cubes
x3 + y3 = (x + y)(x2 – xy + y2)
Copyright © 2010 Pearson Education, Inc. All rights reserved.

11. Factoring Difference of Cubes
7.3 Special Factoring
EXAMPLE 3
Factoring Difference of Cubes
Factor each polynomial. Recall, x3 – y3 = (x – y)(x2 + xy + y2).
(a) a3 – 125

12. Factoring Sums of Cubes
7.3 Special Factoring
EXAMPLE 4
Factoring Sums of Cubes
Factor each polynomial. Recall, x3 + y3 = (x + y)(x2 – xy + y2).
(a) n
(b) 64v g3
Copyright © 2010 Pearson Education, Inc. All rights reserved.

13. Factoring Difference of Cubes
7.3 Special Factoring
EXAMPLE 3
Factoring Difference of Cubes
Factor each polynomial. Recall, x3 – y3 = (x – y)(x2 + xy + y2).
(b) 8g3 – h3
Copyright © 2010 Pearson Education, Inc. All rights reserved.

14. Factoring Difference of Cubes
7.3 Special Factoring
EXAMPLE 3
Factoring Difference of Cubes
Factor each polynomial. Recall, x3 – y3 = (x – y)(x2 + xy + y2).
(c) 64m3 – 27n3
Copyright © 2010 Pearson Education, Inc. All rights reserved.

15. Factoring Sums of Cubes
7.3 Special Factoring
EXAMPLE 4
Factoring Sums of Cubes
Factor each polynomial. Recall, x3 + y3 = (x + y)(x2 – xy + y2).
(c) 2k =
Copyright © 2010 Pearson Education, Inc. All rights reserved.

16. 7.3 Special Factoring Factoring Summary
Special Types of Factoring (Memorize)
Difference of Squares x2 – y2 = (x + y)(x – y)
Difference of Cubes x3 – y3 = (x – y)(x2 + xy + y2)
Sum of Cubes x3 + y3 = (x + y)(x2 – xy + y2)
Copyright © 2010 Pearson Education, Inc. All rights reserved.