1. Special Factoring

2. Difference of Squares General Formula: (x) 2 – (y) 2 = (x + y)(x – y)

3. Example 1: m 2 – 64 = (m) 2 – (8) 2 = (m + 8)(m – 8)

4. Example 2:36x 2 – 49y 2 = (6x) 2 – (7y) 2 = (6x + 7y)(6x – 7y)

5. Example 3:48a 3 – 12a = 12a(4a 2 – 1) = 12a[(2a) 2 – (1) 2 ] = 12a(2a + 1)(2a – 1)

6. 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)

7. Now you try! 1) 9x 2 – 64 = (3x – 8)(3x + 8) = (2x – 4)(2x + 4) 2) 4x 2 – 16 = 2(x + 8)(x + 1) 3) 2x 2 + 18x + 16 = 4(x – 2)(x + 2)

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

9. Difference of Cubes General Formula: (a) 3 – (b) 3 = (a – b)(a 2 + ab + b 2 )

10. Ex: x 3 – 27 = (x) 3 – (3) 3 = (x – 3)(x 2 + 3x + (3) 2 ) = (x – 3)(x 2 + 3x + 9)

11. Sum of Cubes General Formula: (a) 3 + (b) 3 (a + b)(a 2 – ab + b 2 )

12. Ex: c 3 d 3 + 64 = (cd) 3 + (4) 3 = (cd + 4)((cd) 2 – 4cd + (4) 2 ) = (cd + 4)(c 2 d 2 – 4cd + 16)

13. 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)