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What Does FOIL in Math Mean?

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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.
Acronyms
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.

Binomial
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.

Binomial
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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!

F-O-I-L 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.

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

Combining Like Terms
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