1. Factoring Differences of Squares

2. Remember, when factoring, we always remove the GCF (Greatest Common Factor) first. Difference of Squares has two terms Trinomial Square has three terms

3. Factoring Differences of Squares A Trinomial Square Has three terms The first and last term are perfect squares The sign pattern of the terms is + - + or + + + The middle term is twice the product of the square root of the first term and the square root of the last term.

4. Factoring Differences of Squares Example 1: Factor the following polynomials completely. (m + 3) 2 – 9t 2 = W 2 – 9t 2  Let W = m + 3 = (W – 3t)(W + 3t)  W 2 – 9t 2 is a difference of squares = (m + 3 – 3t)(m + 3 + 3t)  sub m + 3 back in for W

5. Factoring Differences of Squares Example 2: Factor the following polynomials completely. y 2 – 10y + 25 – 36v 2 = (y 2 – 10y + 25) – 36v 2  Find the trinomial square = (y – 5) 2 – 36v 2  Factor the trinomial square = W 2 – 36v 2  Let W = y – 5 = (W – 6v)(W + 6v)  Factor the difference of squares = (y – 5 – 6v)(W – 5 + 6v)  sub y – 5 for W

6. Homework Do # 33, 35, 37, 39, 45, 47, 51, 61, and 63 on page 115 for Wednesday