Welcome back, everyone. We already saw how to add and subtract polynomials. And in this video, we're going to start talking about multiplying polynomials. It turns out we've already done some of this stuff before when we looked at the distributive property with expressions and exponents. We saw how to take terms on the outside of parentheses and distribute either constants or variables on the inside, but a lot of problems are not going to look like that. A lot of problems are actually going to start looking like this where you have 2 parentheses that are multiplied together. So a lot of problems are actually going to involve multiplying 2 binomials. Remember, these are just expressions with 2 terms. And so when we have these kinds of problems, we're not going to use the distributive property. We're going to use a new method called the FOIL method, and that's a term you may have heard in a math class somewhere. We're going to go over it, and I'm going to show you that it's actually a very straightforward procedure that tells you exactly what to do and the order. Alright. So let's just go ahead and jump right in.

FOIL is actually just an acronym, and it tells you which two terms to multiply with this expression over here, these 2, these 2 binomials, and it also tells you what order to multiply them in. Alright? So the F O I L, they stand for different things. Let's just jump right into it. The F actually stands for the first terms. So you multiply the first two terms of each expression. Some of the words that would be just the x and the x. The next thing you would do is the O, which is the outer terms. So if you think about this, there's sort of 4 terms in this expression or this multiplication. The outer terms are the 2 terms sort of on the outsides. So the x and the 3. Alright? Now the third thing is you're going to multiply the I, which is the inner terms. That would actually just be the 2 and the x that's on the inside right here. And the very last thing is you multiply the last terms. So you just multiply the 2 and the 3. Notice how every single term gets multiplied by the two terms in the opposite expression, so everything actually gets multiplied by each other. And that's how you sort of do it.

So let's just go ahead and FOIL this expression out. How do you multiply x plus 2 and x plus 3? Well, remember, F means that we're going to multiply the first two terms, the x and the x. What happens when you get that? You just get x^{2}. So let's do the O, which is the outer terms. That would just be the x and the 3. Well, x and 3 multiplied together just becomes 3x. What about the inner terms, the 2 and the x? That's the I. So the 2 and the x just becomes 2x. And finally, the 2 and the 3, those are the last terms. 2 multiplied by 3 just becomes 6, not 6x because they're just two numbers together. Alright? So that's it. That's the whole thing. That's how to FOIL.

The very last thing you have to do is once you FOIL, you're usually going to have to simplify your expression because usually what happens is these middle terms will be like terms, and you'll be able to combine them. Alright? So, in other words, this expression simplifies down to x^{2}. I can't combine that with anything else, but I can combine the 3x and the 2x because they're like terms, and they actually just combine down to 5x. And then finally, you just have the 6 that comes down like this, and that is your simplified expression. So this is how you FOIL 2 binomials and simplify it. Let me know if you have any questions. If not, let's move on to the next video.