## 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:

$\fn_jvn {\color{DarkBlue}(x-2)(x^2+3x+3)}$

## 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.

$\fn_jvn {\color{DarkBlue}x(x^2+3x+3)=x^3+3x^2+3x}$

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

$\fn_jvn {\color{DarkBlue}-2(x^2+3x+3)=-2x^2-6x-6}$

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

$\fn_jvn {\color{DarkBlue}x^3+3x^2+3x}\\ {\color{DarkBlue} \hspace{1.24cm}-2x^2-6x-6}$

$\fn_jvn {\color{DarkBlue}x^3+x^2-3x-6}$