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The FOIL Method

The FOIL Method

Author: Anthony Varela
Description:

Multiply two binomials by using the FOIL method.

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Tutorial

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Hello, and welcome. My name is Anthony Varela. And today, we're going to talk about the FOIL method. So what we'll do first is review how to distribute something that looks like this. Then we'll step it up a notch and talk about how to distribute something that looks a little more complicated. And through this, we're going to develop a process called "FOILing." So we're going to practice then FOILing some expressions.

So let's review our distributive property. Now, our distributive property states that we can have this factor outside of a sum. And we can distribute it into each addend in that sum. So we can distribute a into b and a into c to get an equivalent expression, ab plus ac.

So let's go through a concrete example. Here, I have 3 times 5 plus 7. Now I'm going to do this following the order of operations just to show that I know what I'm looking for at the end. I know that I'm looking for 36. But let's do this using distribution.

So first, I'm going to multiply 3 by five to get 15. Then I'm going to distribute the 3 into the 7. So 3 times 7 is 21. When I add these two together, I get 36. So that's what we mean when we're applying our distributive rule.

But now let's talk about something a little bit more complicated-- multiplying two binomials and a "binomial" is just a fancy word for an expression that has two terms. So here's one binomial multiplied by another.

So first what I'm going to do again is I know that 7 plus 4 is 11 and 8 plus 3 is 11. So I know in the end I am looking for 121. But let's do this a different way.

And it might seem like we're doing it a longer, harder way. But when you are studying quadratic equations and you put variables into the mix, you're really going to want to know how to FOIL. So it might seem like the long way right now. But it'll pay off in the end.

And what I'm going to do first is I'm going to distribute the 7 into 8 and 3. So I'm going to multiply 7 times 8 to get 56. Then I'll multiply 7 by 3 to get 21.

So now I have to distribute again. I'm going to distribute the 4 into 8 and 3. So 4 times 8 is 32. And then 4 times 3 is 12. And I'm going to add all of these values together, and I get 121.

And now let's take a closer look at exactly what we were doing. Well, when we were multiplying the 7 in the 8, we were multiplying the first terms in each of these factors, 7 and 8. When we multiplied the 7 and a 3, we were multiplying the outermost terms.

And then when we multiplied the 4 and the 8, we were multiplying the inside terms. And, finally, when we multiplied 4 and 3, we are multiplying the last terms. And that's how we come up with FOIL. So FOIL is an acronym to remember the steps for distributing factors in binomial multiplication. And those steps are the first terms, the outside terms, the inside, and then the last ones.

So now let's practice FOILing. So here is our expression. 3 plus 5, we're multiplying that by the quantity 8 minus 4. So first I'm going to multiply the 3 and the 8. That gives me 24. Then I'm going to multiply the outside terms. So we have 3 times negative 4. Watch out for the negative. So I get negative 12 here.

Then I'm going to multiply the inside, which is 5 times 8. That gives me 40. And lastly, I'm going to multiply the last terms, 5 times negative 4. That gives me negative 20.

Now I add all of these together. And I get, let's see, 24 plus negative 12 is 12. 40 plus negative 20 is 20. So when you add those two, I get 32.

Let's check to see if we did this right. I know that 3 plus 5 is 8. And 8 minus 4 is 4. And, sure enough, we get 32. So we've done our process correctly.

Let's go through one more example. So first, we're going to multiply the negative 8 and 12. So that gives us a negative 96. Then we're going to multiply our outside terms, negative 8 and negative 7 gives as a positive 56.

Then we're going to multiply the inside, which is 2 times 12 to get 24. And then we'll multiply the last terms, 2 times negative 7 to give me negative 14.

We need to add all of these up. So I like to do it in chunks. I know that negative 96 plus 56 is a negative 40. And 24 minus 14 is 10. When we add those together, we get negative 30.

Let's check to see if we've done this right. I know that negative 8 plus 2 is negative 6. 12 minus 7 is 5. So negative 6 times 5 is negative 30. We've done our FOILing correct.

All right. So what did we talk about Today We talked about the FOIL method. And we started off by talking about distribution. And then we talked about FOIL as being an acronym to remember the steps in binomial multiplication-- first, outside, inside, last. And so here is an example then of our binomial multiplication. We multiply the first terms, then the outside terms, then the inside terms, and the last terms.

Well, thanks for watching this tutorial on the FOIL method. Hope to catch you next time.

Terms to Know
FOIL

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