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Multiplying Polynomials: Special Cases - Problem 2

Teacher/Instructor Alissa Fong
Alissa Fong

MA, Stanford University
Teaching in the San Francisco Bay Area

Alissa is currently a teacher in the San Francisco Bay Area and Brightstorm users love her clear, concise explanations of tough concepts

Before I even start doing this problem, I know I have something special because I have the same 2 monomials; the only difference is here I have a minus sign, and here I have a plus sign. So we’re going to see that the middle 2 terms of my Foiling are going to be eliminated, let’s do it.

My first, outers, inners, last is going to be the process I’m going to use that’s what FOIL stands for. First I’m going to get 9a² outers is 3a times 2b, so that’s going to be +6ab. Inners -2 times 3 is -6, and then instead of writing b and then a, I’m going to flip that and write it as a, be because of multiplying it’s okay b times a, is the same thing as a times b so I wrote it like that. Then my last I have -4b².

The reason this is a unique problem, or why this is a special case is because look I have additive inverses. When I add together -6ab and -6ab those cancel out, it becomes 0, so my final answer just looks like 9a² take away 4b². That’s my final answer. Later on and you’ll start talking about why this is called the Difference of Perfect squares. For now it’s okay to know this is just a special product and it happened because I had the same terms, the only difference was that one was negative and one was positive.

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