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Math for Kids23 chapters | 325 lessons

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!

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.

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!

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!

The first example had two binomials with addition signs. Let's try an example where one of the binomials has a subtraction sign! Let's multiply (*x* + 10) (*x* - 2). Using the FOIL method, we multiply the first terms and have (*x*) (*x*) = *x*^2. We multiply the outside terms and have (*x*) (-2) = -2*x*. We multiply the inside terms and have (10) (*x*) = 10*x*. We multiply the last terms and have (10) (-2) = -20. So we have *x*^2 - 2x + 10*x* - 20. Now all we have to do is combine like terms. There are two like terms here. The terms -2*x* and 10*x* are like terms because they both have an *x*. So adding those two like terms we have -2*x* + 10*x* = 8*x*. So our final answer is *x*^2 + 8*x* - 20.

FOIL is a well-known **acronym** in mathematics that is used to multiply two **binomials**. Each binomial has two terms, which include a number and **variable**, that are separated by an addition or subtraction sign. When you multiply using the FOIL method, you multiply the first terms, the outside terms, the inside terms, and the last terms, and then you add those products for your answer!

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Math for Kids23 chapters | 325 lessons

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