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How to Factor a Difference of Squares

When you FOIL (multiply the first, outside, inside, and last terms together) a binomial and its conjugate, the product is called a difference of squares. The product of (ab)(a + b) is a2b2. Factoring a difference of squares also requires its own set of steps.

You can recognize a difference of squares because it’s always a binomial where both terms are perfect squares and a subtraction sign appears between them. It always appears as a2b2, or (something)2 – (something else)2. When you do have a difference of squares on your hands — after checking it for a Greatest Common Factor (GCF) in both terms — you follow a simple procedure: a2b2 = (ab)(a + b).

For example, you can factor 25y4 – 9 with these steps:

  1. Rewrite each term as (something)2.

    This example becomes (5y2)2 – (3)2, which clearly shows the difference of squares (“difference of” meaning subtraction).

  2. Factor the difference of squares (a)2 – (b)2 to (a – b)(a + b).

    Each difference of squares (a)2 – (b)2 always factors to (ab)(a + b). This example factors to (5y2 – 3)(5y2 + 3).

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