Special Cases of Factoring

1. Chapter 5.5 Special Cases of Factoring Difference of Two Squares = a2 – b2 (a + b)(a – b)

2. Difference of Two Squares 1. Check each term to see if there is a GCF of all terms. 2. Write each term as a square. 3. Write those values that are squared as the product of a sum and a difference. = a2 – b2 (a + b)(a – b)

3. 0 1. Factor. 64x2 – 1 1 1. GCF = 2. Write as squares 8x 1 ( )2 – ( )2 3. (sum)(difference) (8x – 1) (8x + 1)

4. 0 2. Factor. 36x2 – 49 1 1. GCF = 2. Write as squares 6x 7 ( )2 – ( )2 3. (sum)(difference) (6x – 7) (6x + 7)

5. 0 3. Factor. 100x2 – 81y2 1 1. GCF = 2. Write as squares 10x 9y ( )2 – ( )2 3. (sum)(difference) (10x – 9y) (10x + 9y)

6. 0 4. Factor. x8 – 1 1 1. GCF = x4 1 ( )2 – ( )2 2. Write as squares x4 – 1 ( ) (x4 + 1) 3. (sum)(difference) ( )2 ( )2 – x2 1 (x2 – 1) (x2 + 1) (x4 + 1) (x2 + 1) (x – 1) (x4 + 1) (x + 1)

7. 0 9. Factor. 20x2 – 45 5 1. GCF = 2. Write as squares 5( ) 4x2 – 9 2x 3 ( )2 – ( )2 3. (sum)(difference) (2x – 3) (2x + 3) 5

8. Chapter 5.5 Special Cases of Factoring Difference of Two Squares = a2 – b2 (a + b)(a – b)