 And welcome back today. We're going to talk about multiplying polynomials. I'm going to do a couple of different videos over this I'm going to start with the the simple stuff first make a separate video for something a little bit more complicated and the the harder ones The expanding polynomials I do a third video on that anyway multiplying a monomial and a polynomial These are the easiest of the multiplying polynomial examples that I'll do As you can see here a couple of examples that I have this is for y squared times The quantity y plus 3 again a monomial times a polynomial a little bit more specific Mono is 1 so this is a single term times a binomial, which is two terms Okay, now what we're doing here is basically this is just a Application of your distributive property. We're just going to take this for y squared and we're going to distribute it to everything That's in the parentheses said that that's basic. Again. This is your basic type of the multiplication Now the one thing that we have to remember though It was when we take this term times everything in the parentheses We have to remember that when we multiply exponents together Excuse me when we multiply variables together the exponents are going to increase they're going to go up Okay, so if I take four y squared times y squared I get four y to the fourth Okay, the rule is when I multiply when I multiply variables The exponents are going to add together now the more and more you do this You realize oh if I'm multiplying exponents. I'm going to go one step down. I'm ready to add them together That's kind of how I remember it anyway, but anyway So if my first term here for y squared times y squared is for y to the fourth for y squared times three is going to be a 12 y squared notice only the coefficient change that time. It was just the number in front nothing else Okay, and then to the right side. I have another example here I'm not gonna use a lot of the space down here. These are mostly one-step problems But anyway, there's another example that I have Looks like the fonts changed a little bit. That doesn't matter. Anyway, this is a monomial, but we got two variables here So this monomial times this one here. This is a one two three four four term polynomial Okay, it's basically the same thing We're just going to take this term and multiply it times everything inside the parentheses So my first multiplication fg times f to the fourth Well, we just concentrate on the f's here because there's no G's so f to the first times f to the fourth is going to be f to the Fifth okay add those exponents together. There is a one here. I just like the G. There is a one there We usually don't write it. That's just one of the things we understand that there is a one for an exponent there So anyway f to the fifth and then G to the first just gonna write that as G Okay, so there's my first multiplication now to move on my second multiplication Do the numbers first this is just going to be a two out front then do the f's f Times f to the third is f to the fourth again one plus four And then the G's G to the first times G to the first is going to be G square G of the second there We go all right and then just keep on keep on trucking take fg times the third So it's going to be negative three now notice that it's it's just f and G We're just increasing everything by one and you can kind of see that from the previous ones f got increased by one G Which actually wasn't there, but still got increased by one F to the third we came after the fourth G to the first came G to the second I mean everything the f's and the G's are just increasing by one because that's what we're multiplying by just one of the F's And one of the G's so actually this is just going to be f to the third and G to the third and this last one is plus F to the second G to the fourth and see once I realized that pattern It was it was real easy to get that very light though that second third or second third excuse me the third and the fourth Multiplications back here. So that was pretty easy to do anyway That's how to multiply a monomial and a polynomial I brought simply straightforward process the one thing you got to remember is that when you multiply variables So if I take x squared times x to the third When I multiply my variables together I have to take the exponents and add them together to get x in this case to the fifth That's just the one thing you had to remember here. So those exponent rules sometimes sometimes we forget those It's been a while since we used them, but anyway, that's that's it for monomium or multiplying monomials and polynomials We'll see you in the next video and thank you for watching