**Multiplying Binomials (F.O.I.L. Method)**

This tutorial will provide a method for multiplying two binomials. Recall that a binomial is defined as a polynomial with exactly two terms. Here are some examples of binomials:

The goal of this tutorial is to learn how to find the product of two of these expressions. The method usually used is called the F.O.I.L. method and it is a mnemonic device designed to remind one of which terms must be included in the product. It arises from the use of the distributive property. The letters stand for the following:

F: Product of the

First two terms in each binomial.

O: Product of theOutside two terms.

I: Product of theInside two terms.

L: Product of theLast two terms in each binomial.

Here’s an example of how it’s done with two simple expressions. Say we wanted to find the product:

F O I L

(a+b)(c+d) =a•c+a•d+b•c+b•d

Then we just add them up and the solution is:

So you see that multiplying two binomials gives us four terms. Often times, however, some of the terms will be *like terms* which can be combined to simplify the result (see tutorial on Simplifying Expressions for a review if necessary) as in the following example.

__Example __

Use the F.O.I.L. method to find this product:

__Solution __

F O I L

(3*x* – 8)(2*x* + 3) = (3*x*)(2*x*) + (3*x*)(3) + (-8)(2*x*) + (-8)(3)

It is important to make sure that the signs are correct when carrying out these operations. Note that the sign in front of a given term stays with that term when carrying out the multiplication.

The four terms are:

6*x*^{2} + 9*x* – 16*x* - 24

Next combine the four terms to get the simplified product: