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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 the Outside two terms.
I: Product of the Inside two terms.
L: Product of the Last 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) =         ac    +          ad    +          bc    +          bd

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

6x2 + 9x – 16x - 24

Next combine the four terms to get the simplified product: