1. Section 6.3 Special Factoring

2. Overview In this section we discuss factoring of special polynomials. Special polynomials have a certain number of terms. The terms have special characteristics. As a result, these special polynomials can be factored by using patterns.

3. The Difference of Squares a 2 – b 2 = (a + b)(a – b) The first term is a perfect square The last term is a perfect square There is a subtraction sign between the terms 1, 4, 9, 16, 25, 36, 49, 64, 81, 100,… Variables with even exponents The sum of squares, a 2 + b 2, does not factor!

4. Examples k 2 – 9 36m 2 – 25 32c 2 – 98d 2 (h + k) 2 – 9

5. The Sum and Difference of Cubes a 3 + b 3 = (a + b)(a 2 – ab + b 2 ) a 3 – b 3 = (a – b)(a 2 + ab + b 2 ) The first term is a perfect cube The last term is a perfect cube 1, 8, 27, 64, 125, 216, 343, 512, 729, 1000,… Variables with exponents that are multiples of 3 The trinomial in the pattern is prime!

6. Examples y 3 – 64 r 3 + 343 64g 3 – 27h 3 250x 3 + 16y 3

7. Perfect Square Trinomials a 2 + 2ab + b 2 = (a + b)(a + b) = (a + b) 2 a 2 – 2ab + b 2 = (a – b)(a – b) = (a – b) 2 The first term is a perfect square The last term is a perfect square The last sign is positive Warning: check it by FOIL! Other trinomial factoring methods will work on these as well.

8. Examples x 2 + 10x + 25 9y 2 – 6yz +z 2 (a – b) 2 + 8(a – b) + 16

9. Don’t Forget!!! Always first look for a GCF!!!!!