Trigonometry For Dummies
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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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Mary Jane Sterling taught algebra, business calculus, geometry, and finite mathematics at Bradley University in Peoria, Illinois, for more than 30 years. She is the author of several For Dummies books, including Algebra Workbook For Dummies, Algebra II For Dummies, and Algebra II Workbook For Dummies.

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