Chapter 7 Factoring

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.

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.

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.

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 x2 + 16. Copyright © 2010 Pearson Education, Inc. All rights reserved.

Factoring Perfect Square Trinomials 7.3 Special Factoring EXAMPLE 2 Factoring Perfect Square Trinomials Factor each polynomial. (a) 9g2 – 42g + 49 Copyright © 2010 Pearson Education, Inc. All rights reserved.

Factoring Perfect Square Trinomials 7.3 Special Factoring EXAMPLE 2 Factoring Perfect Square Trinomials Factor each polynomial. (b) 25x2 + 60xy + 64y2 Copyright © 2010 Pearson Education, Inc. All rights reserved.

Factoring Perfect Square Trinomials 7.3 Special Factoring EXAMPLE 2 Factoring Perfect Square Trinomials Factor each polynomial. (d) c2 – 6c + 9 – h2

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

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

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

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) n3 + 8 (b) 64v3 + 27g3 Copyright © 2010 Pearson Education, Inc. All rights reserved.

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.

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.

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) 2k3 + 250 = Copyright © 2010 Pearson Education, Inc. All rights reserved.

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.