 This video is called subtracting polynomials. To subtract polynomials is just a little bit more work than adding polynomials. We know that this is a subtraction problem because I have a polynomial, a subtraction sign, and then another polynomial. It's this subtraction sign between the two polynomials that let me know, that lets me know it's a subtraction problem. It's important to pay attention to that. I know it seems like a simple thing, but you have to know what you're supposed to be doing. Adding, subtracting, or multiplying. This case, it's subtracting. When you subtract, you look between the subtraction sign and the first set of parentheses, and there's really a one there. So there's a negative one that needs to be distributed to everything in the second set of polynomials. So basically, when you multiply everything by a negative one, the signs of those three terms will just switch. So to start, rewrite your first polynomial exactly how it's given to you. Then, let's distribute that negative one. Negative one times x cubed is negative x cubed. Negative one times negative 8x squared is a plus 8x squared, and negative one times 11 is a minus 11. Now that I've distributed that negative one, it's time to combine like terms. I've got a plus 2x to the third and a minus x to the third. Remember, there's a one between the negative and the x. So 2x cubed minus 1x cubed is x cubed. A plus 5x squared and a plus 8x squared are like terms. 5 plus 8 is 13. So you have plus 13x squared. Then what comes next? I've got a negative 3x. Well, I don't have any other terms that just have an x behind them, so I'll bring the negative 3x down. And same with my constant. I only have one constant, so there's nothing to combine it with. So that will be a negative 11. So that is your answer to subtract those two polynomials. Notice it is in standard form. The biggest exponent is first, all the way down to the constant. Let's try it. So when I look at this next example again, I recognize it's a subtraction problem because there's a subtraction sign between my two polynomials. So what I'm going to have to do first is distribute that negative one to everything in the second polynomial. So I'll start by rewriting my first one as it was given to me. And then when I write my second one, I'll just basically do the opposite sign. Negative 1 times 9v cubed is negative 9v cubed. Negative 1 times a negative 7v squared is a plus 7v squared. A negative 1 times a positive 3v is minus 3v. So now when I combine my like terms, I'll start with this v cubed. Remember there's really a 1 there. I've got a negative 9v cubed. Well, 1 minus 9 is negative 8, so I have negative 8v to the third. Now I have a positive 6v squared and a positive 7v squared. Well, 6 plus 7 is 13, so I have a positive 13v squared. Now this guy is a negative v. There's really a 1 there, so it's negative 1v and I have a negative 3v. Well, negative 1 minus 3 is a negative 4v. And I look, I think I've taken care of everything. So negative 8v cubed plus 13v squared minus 4v is the answer to subtracting those two polynomials.