Method

The FOIL Method

The FOIL method is a mnemonic for remembering how to multiply two binomials. The word FOIL is an acronym for the words

F irst,

O uter,

I nner,

and

L ast .

Consider, for example, the following product.

(x + 6) (3 x - 2)

These two binomials can be multiplied by following five steps.

Multiply the First Terms

Start by multiplying the first terms of each binomial. In this case, multiply

x

3 x .

(x + 6) (3 x - 2) = x (3 x) - 2 x + 18 x - 12

The empty box is there as a reminder that there are still missing terms.

Multiply the Outer Terms

Next, multiply the outer terms — that is, multiply the first term of the left-hand side binomial by the second term of the right-hand side binomial. In this case, multiply

x

- 2 .

(x + 6) (3 x - 2) = x (3 x) + x (- 2) 18 x - 12

Multiply the Inner Terms

Now multiply the inner terms — that is, multiply the second term of the left-hand side binomial by the first term of the right-hand side binomial. In this case, multiply

6

3 x .

(x + 6) (3 x - 2) = x (3 x) + x (- 2) + 6 (3 x) - 12

Multiply the Last Terms

Next, multiply the last terms of each binomial — that is, multiply the second term of the left-hand side binomial by the second term of the right-hand side binomial. In this case, multiply