Factoring Differences of Squares

Factoring Differences of Squares

Remember, when factoring, we always remove the GCF (Greatest Common Factor) first.

Difference of Squares has two terms

Trinomial Square has three terms

Factoring Differences of Squares

A Trinomial SquareHas three termsThe first and last term are perfect squaresThe 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.

Factoring Differences of Squares

Example 1: Factor the following

polynomials completely.

(m + 3)2 – 9t2

= W2 – 9t2 Let W = m + 3= (W – 3t)(W + 3t) W2 – 9t2 is a

difference of squares

= (m + 3 – 3t)(m + 3 + 3t) sub m + 3 back in for W

Factoring Differences of Squares

Example 2: Factor the following

polynomials completely.

y2 – 10y + 25 – 36v2

= (y2 – 10y + 25) – 36v2 Find the trinomial square

= (y – 5)2 – 36v2 Factor the trinomial square

= W2 – 36v2 Let W = y – 5

= (W – 6v)(W + 6v) Factor the difference of squares

= (y – 5 – 6v)(W – 5 + 6v) sub y – 5 for W

Homework

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