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Math for Kids23 chapters | 325 lessons

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Lesson Transcript

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'll review the meaning of FOIL - not the foil used in the kitchen - but instead the series of four steps used when multiplying two binomials, or terms separated by an operational sign.

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

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

We know that this is a binomial because 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 because we have two terms that are separated by an addition sign. One easy way to multiply two binomials is to use the FOIL method!

The FOIL method is made up of four multiplication steps. 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 place each of the binomials in its own parentheses. Next, using the FOIL method, multiply the first terms from each binomial together. Now, multiply the outside terms of each binomial together. Then, multiply the inside terms together. Finally, 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, which gives us (*x*) (*x*) = *x*^2. Next, we multiply the outside terms and have (*x*) (-2) = -2*x*. Now, we multiply the inside terms and have (10) (*x*) = 10*x*. Finally, 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. Here, -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.

Let's review! An **acronym** is a common word or abbreviation where all of the letters stand for another word. **FOIL** is a well-known **acronym** in mathematics that is used to multiply two **binomials**, which are numbers or variables. Each binomial has two terms, which include a number and **variable**, or a letter that stands for something, that are separated by an addition or a subtraction sign. When multiplying using the FOIL method, multiply the first terms, the outside terms, the inside terms, and the last terms, and then add those products to obtain the answer!

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Math for Kids23 chapters | 325 lessons

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