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

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

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

4. Copyright © 2010 Pearson Education, Inc. All rights reserved. Special Factoring Caution CAUTION Assuming no greatest common factor except 1, it is not possible to factor (with real numbers) a sum of squares, such as x 2 + 16.

5. Copyright © 2010 Pearson Education, Inc. All rights reserved. Special Factoring EXAMPLE 2Factoring Perfect Square Trinomials Factor each polynomial. (a) 9 g 2 – 42 g + 49

6. Copyright © 2010 Pearson Education, Inc. All rights reserved. Special Factoring EXAMPLE 2Factoring Perfect Square Trinomials Factor each polynomial. (b) 25 x 2 + 60 xy + 64 y 2

7. Special Factoring EXAMPLE 2Factoring Perfect Square Trinomials Factor each polynomial. (d) c 2 – 6 c + 9 – h 2

8. Copyright © 2010 Pearson Education, Inc. All rights reserved. Special Factoring Difference of Cubes x 3 – y 3 = ( x – y )( x 2 + xy + y 2 )

9. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 7.3 - 9 Special Factoring Sum of Cubes x 3 + y 3 = ( x + y )( x 2 – xy + y 2 )

10. Special Factoring EXAMPLE 3Factoring Difference of Cubes Factor each polynomial. Recall, x 3 – y 3 = ( x – y )( x 2 + xy + y 2 ). (a) a 3 – 125

11. Copyright © 2010 Pearson Education, Inc. All rights reserved. Special Factoring EXAMPLE 4Factoring Sums of Cubes Factor each polynomial. Recall, x 3 + y 3 = ( x + y )( x 2 – xy + y 2 ). (a) n 3 + 8 (b) 64 v 3 + 27 g 3

12. Copyright © 2010 Pearson Education, Inc. All rights reserved. Special Factoring EXAMPLE 3Factoring Difference of Cubes Factor each polynomial. Recall, x 3 – y 3 = ( x – y )( x 2 + xy + y 2 ). (b) 8 g 3 – h 3

13. Copyright © 2010 Pearson Education, Inc. All rights reserved. Special Factoring EXAMPLE 3Factoring Difference of Cubes Factor each polynomial. Recall, x 3 – y 3 = ( x – y )( x 2 + xy + y 2 ). (c) 64 m 3 – 27 n 3

14. Copyright © 2010 Pearson Education, Inc. All rights reserved. Special Factoring EXAMPLE 4Factoring Sums of Cubes Factor each polynomial. Recall, x 3 + y 3 = ( x + y )( x 2 – xy + y 2 ). (c) 2 k 3 + 250 =

15. Copyright © 2010 Pearson Education, Inc. All rights reserved. Special Factoring Factoring Summary Special Types of Factoring (Memorize) Difference of Squares x 2 – y 2 = ( x + y )( x – y ) Difference of Cubes x 3 – y 3 = ( x – y )( x 2 + xy + y 2 ) Sum of Cubes x 3 + y 3 = ( x + y )( x 2 – xy + y 2 )