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The FOIL Method

The FOIL Method

Author: Colleen Atakpu

This lesson introduces a common method to multiplying two binomials.

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Video Transcription

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Today, we're going to talk about the FOIL method. The FOIL method is used to multiply groups of numbers together. And it's based off of the distributive property. So we're going to start by reviewing the distributive property, and then we'll do some examples using the FOIL method.

So as I said, the FOIL method is related to the distributive property. So let's start by reviewing that. Our distributive property tells us that a times b plus c is the same as a times b plus a times c. So you're distributing this factor, a, to both numbers inside the parentheses. So if we put some numbers with that-- if I've got 5 plus 2 plus 3, 2 plus 3 gives me 5. And if I multiply it by the 5 on the outside, that gives me 25.

So if we look at this side, this should also equal 25. So a times b would be 5 times 2. a times c would be 5 times 3. 5 times 2 gives me 10, and 5 times 3 will give me 15. Adding 10 and 15 together, I see that I still get 25. So we can extend this distributive property to multiply groups of numbers.

These are called binomials. There are two terms, or two numbers, in each set of parentheses. So we can use the FOIL method to distribute when we're multiplying binomials. And the idea behind that is that, if I'm multiplying a and b by c and d, I need to distribute the a to both c and d, or multiply a by both c and d. And I need to multiply b by both c and d.

So by looking at those four products, I've got a times c, plus a times d, plus b times c, plus b times d. So if we look at an example with numbers, we can see that, let's say I've got 2 plus 6, times 3 plus 4. So 2 plus 6 will give 8, 3 plus 4 will give me 7, and 8 times 7 gives me 56.

So on this side, I've got a times c, which would be 2 times 3. a times d, which would be 2 times 4. Now I'm going to multiply my b times c, so 6 times 3. And I'm going to multiply my b times d, so 6 times 4. 2 times 3 is 6. 2 times 4 is 8. 6 times 3 is 18. 6 times 4 is 24. Adding these together, 6 plus 8 will give me 14. 14 plus 18 is going to give me 32. And 32 plus 24 does give me 56.

So we can see that the FOIL method also works. And so what FOIL actually stands for is First Outer Inner and Last. So where those words come from is a and c are my first terms in each parentheses. So first. a and d are my outer terms in my parentheses, so a is on the outside and d is on the outside. My b and c are my inside terms. b and c are both on the inside. And my b and d are both the last term in each parentheses.

So let's do a couple of examples using the FOIL method. For my first example, I've got 3 plus 2 times 4 minus 1. So you can see that when we're using FOIL, we can have either addition or subtraction inside of our parentheses. And we're going to think of this as a negative 1, so we'll be multiplying by negative 1.

All right, so using FOIL, I know that I need to multiply my first, outer, inner and last terms. So my first terms are going to be 3 times 4, which is going to give me 12. My outside terms are 3 and negative 1. So that's going to give me a negative 3. My inside terms are 2 times 4. So that's going to give me 8. And my last terms are 2 times negative 1, or negative 2. Summing these numbers up, 12 plus a negative 3 will give me 9. 9 plus 8 is going to give me 17. And 17 plus a negative 2 will give me 15.

All right. Let's try a second example. Again, here we have a subtraction sign, and we know that we're going to think of this as a negative 1. So using my FOIL method, I'm going to start by multiplying my first two terms together, so 7 times 3 will give me 21. I'm then going to multiply my outer terms together. So 7 times 4 will give me 28. Multiply my inside terms, negative 1 times 3 will give me a negative 3. And multiplying my last terms together, negative 1 times 4 will give me negative 4.

So now we're going to sum these four numbers up. 21 plus 28 will give me 49. 49 plus a negative 3 will give me 46. And 46 plus a negative 4 will give me 42. All right. Let's go over our key points. Make sure that you get these in your notes, if you don't have them already, so you can refer to them later.

So we talked about the FOIL method as being a method of distributing when you're multiplying groups of terms that look like this. These again are called binomials. So if we're multiplying a plus b times c plus d, multiplying two binomials. And we use the FOIL acronym to help us remember the steps for doing that distributing.

So FOIL stood for First Outer Inner and Last. So I hope that these examples and key points helped you understand a little bit more about the FOIL method. Keep using your notes and keep on practicing, and soon you'll be a pro. Thanks for watching.

Terms to Know

An acronym to remember the steps for distributing factors in binomial multiplication: first, outside, inside, last.

Formulas to Know
FOIL Method

open parentheses a plus b close parentheses open parentheses c plus d close parentheses equals a c plus a d plus b c plus b d