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Multiplying a Binomial by a Trinomial

This post about multiplying a binomial by a trinomial is part of a series of posts to help you prepare for the Advanced Algebra and Functions part of the Accuplacer test.

Question

Multiply:


Solution

The first expression — the contents of the first set of parentheses — is called a binomial because it has two terms. The second expression — the contents of the second set of parentheses — is called a trinomial because it has three terms. To multiply a binomial  by a trinomial, multiply each term in the binomial by each term in the trinomial.

You need a way to organize this. Try this: Multiply x, the first term in the binomial, by each term in the trinomial. Then multiply -2, the second term in the binomial, by each term in the trinomial. Then add all those results together.

  • Multiply x, the first term in the binomial, by each term in the trinomial.

  • Multiply -2, the second term in the binomial, by each term in the trinomial.

  • Add the results, adding like terms to like terms. If you stack the expressions vertically, that will help you keep like terms lined up:

That adds up to:

And that’s the answer.

This question is similar to question number 4 in the sample questions for the Accuplacer Advanced Algebra and Functions test.