What Does FOIL in Math Mean?

Instructor: Allison Petrovic

Allison has experience teaching high school and college mathematics and has a master's degree in mathematics education.

In this lesson we will go over what FOIL means. I am not talking about the foil used in a kitchen! We will learn how useful and simple this method is when multiplying two binomials!

A Math Acronym!

LOL! BFF! NFL! ABC! NASA! These are just a few popular acronyms that you may know. An acronym is a common word or abbreviation where all of the letters stand for another word. So in LOL, the first 'L' stands for laugh, the 'O' stands for out, and the last 'L' stands for loud. So we get laugh out loud. One of math's most popular acronyms is FOIL. Before we learn what each letter stands for in FOIL, we need to look at one important word.

What is a Binomial?

A binomial is made up of two numbers or variables, also known as terms, that are separated by an addition or subtraction sign. Remember that a variable is a letter that stands for something. Let's look at the binomial image.


We know that this is a binomial since we have two terms that are separated by a plus sign. The x is a variable! Another example of a binomial is x + 1. We know that this is a binomial since we have two terms that are separated by an addition sign. One thing that we can do with binomials is multiply them together. One easy way to multiply two binomials is to use the FOIL method!

The F-O-I-L Method

When we multiply two binomials, we can use the FOIL method. The FOIL method is made up of four multiplication steps. Each step goes with each letter in FOIL. Let's see what each letter in FOIL stands for one a time. The 'F' stands for first. The 'O' stands for outside. The 'I' stands for inside, and the 'L' stands for last.

To use the FOIL method, the first thing you need to do is put each of the binomials in their own parentheses. Then, using the FOIL method, multiply the first terms from each binomial together first. Then, multiply the outside terms of each binomial together second. Multiply the inside terms together third. Last, multiply the last terms of each binomial together.


Then, combine like terms and add all of the products and you have your answer!

Combining Like Terms

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