 So we'll close the section on polynomial products by introducing a bad method for multiplying polynomials. If you want to do yourself a favor, skip this video. Still here? All right, you've been warned. So the key to multiplying polynomials is the distributive property applied as many times as necessary. And the key to remember is that every term in one factor must be multiplied by every term in the other factor. And as long as you remember this, you can also find polynomial products without drawing pictures. But why would you want to? And again, I'll give you one last chance to skip this video. Really? You're still here? Eh, well, you've been warned twice. So here is a bad method of multiplying polynomials. You might have been taught something called FOIL. And the idea here is that if I have a product like x plus a times x plus b, in order to perform this multiplication of every term in the first factor by every term in the second factor, what we can do is we can multiply our first terms together. That's x times x. What are called the outer terms together, x times b, are inner terms, a times x, and our last terms, a times b. And you can use this on the product of two binomials. Unfortunately, you can't actually use it on anything else. So 8x times x plus 7, this is not the product of two binomials. We can't use FOIL. x squared plus 3x plus 2 times 2x plus 5, this is not the product of two binomials, so we can't use FOIL. Is there anything we could use FOIL on? Sure, it has to be a product of two binomials. So, for example, x plus 3 times 2x plus 5. The thing to remember is that FOIL works in the very, very, very unusual situation where you have a problem where FOIL works. And if I was a kind and gentle math teacher, then every problem I gave you would be one that FOIL worked on. Unfortunately for you, I am neither kind nor gentle. So while FOIL does work in problems that are written to make use of FOIL, don't count on it to multiply two binomials. So again, remember FOIL is a bad method of multiplying two binomials. Nevertheless, there is still the expectation in certain circles that you'll be able to multiply two binomials using FOIL. So, here's a quick example. If I want to find the product x plus 3 times 2x plus 5, I'll multiply my first terms together. That's x by 2x. I'll multiply the outer terms together. That's x by 5. I'll multiply the inner terms 3 by 2x. And finally, I'll multiply the last terms together 3 by 5. And I'll find those products and collect like terms to simplify.