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.