Hi, my name is Bassem Saad. I'm a Math Ph.D. candidate at U.C. Davis, and I'm here today for About.com to show you how to use FOIL to multiply binomials.FOIL is a mnemonic device to help you remember how to multiply two polynomials. The letters stand for: First; Outside; Inside; Last. Let me demonstrate for you right here. With this polynomial we would multiply the first two numbers, then the outside two numbers, then the inside two numbers, then the last two numbers – FOIL.Let's take a look at another example. Here we have two polynomials, so we'll use FOIL again. That is, we multiply first, which is three times one, which just gives us three. We multiply outside, which is three times minus x, which just gives us minus three x. We multiply inside, which is just x times one -- gives us plus x.And we multiply last, which is just x times minus x -- gives us minus x squared. We then combine like-terms and we'll have our result. So, there are no other threes; we leave it alone. But here we have two different x's. We add their coefficients: minus three, plus one, gives us minus two x. And we end with minus x squared.Let's take a look at another example. We have two polynomials so we'll use FOIL again. That is, we have first times first, which is just y. Then we do outside, which is one times one, which is plus one.Then we do inside, which is minus y times y, which is minus y squared. And finally, we have last: minus y times one, which is minus y. Now we can combine like-terms. So y, we have another minus y. We combine their coefficients – one minus one is zero. So we have zero in front of our y (you don't have to write it down). Then we have one minus y squared. Now we have our solution.Let's talk real world applications. Physicists and biologists need to be able to multiply binomials regularly and the FOIL method can help. Even contractors can use FOIL to help them plan their projects. Thanks for watching, and to learn more, visit us on the web at About.com.

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