1. Tuesday, July 1 Special Factoring

2. Difference of Squares Example: m 2 – 64 (m) 2 – (8) 2 (m + 8)(m – 8)

3. Example 2:36x 2 – 49y 2 (6x) 2 – (7y) 2 (6x + 7y)(6x – 7y) Example 3:48a 3 – 12a 12a(4a 2 – 1) 12a((2a) 2 – (1) 2 ) 12a(2a + 1)(2a – 1)

4. Example 4:2x 4 – 162 2(x 4 – 81) 2((x 2 ) 2 – (9) 2 ) 2(x 2 + 9)(x 2 – 9) 2(x 2 + 9)((x) 2 – (3) 2 ) 2(x 2 + 9)(x + 3)(x – 3)

5. Now you try! Example: 4y 4 - 2500 Example: 5x 3 + 15x 2 – 5x – 15 4(y 2 + 25)(y + 5)(y – 5) 5(x + 1)(x – 1)(x + 3)

6. Sum of Squares General Formula: (x) 2 + (y) 2 PRIME!!! Cannot be factored

7. Difference of Cubes General Formula: (a) 3 – (b) 3 (a – b)(a 2 + ab + b 2 ) Example:x 3 – 27 (x) 3 – (3) 3 (x – 3)(x 2 + 3x + (3) 2 ) (x – 3)(x 2 + 3x + 9)

8. Sum of Cubes General Formula: (a) 3 + (b) 3 (a + b)(a 2 – ab + b 2 ) Example: c 3 d 3 + 64 (cd) 3 + (4) 3 (cd + 4)((cd) 2 – 4cd + (4) 2 ) (cd + 4)(c 2 d 2 – 4cd + 16)

9. Perfect Square Trinomials General Formula: (a) 2 + 2ab + (b) 2 (a + b) 2 General Formula: (a) 2 – 2ab + (b) 2 (a – b) 2

10. Example:x 2 – 12x + 36 (x) 2 – 2·x·6 + (6) 2 (x – 6)(x – 6)

11. Factoring Review