 This video is going to talk about adding and subtracting polynomials. Alright, so if I want to add polynomials, the idea is to group your like terms together and then add the coefficients of the like terms. We're going to keep the variable, all we have to add are the coefficients. So if I wanted to, I could rewrite this as 2A plus 4A, and then add my 4, which is a constant, and then subtract my 8, which is also a constant. And now you can see that we have 8 terms and constant terms. So I'm going to combine these. 2A plus 4A is going to give me a total of 6A, and 4 minus 8 will be minus 4. There, 6A minus 4 is a solution when we add. And this one, I'm going to combine my like terms if I have them, and I'm going to rewrite my like terms together. 5x squared is the only x squared term. And I'm going to cross these off so I know that I've used them. Here I have an x, and here I have an x over here. So I'm plus x, and then minus 3x, and then I've got my constants. So minus 12 and plus 6. So now I've got all my like terms together. I've got only one x squared. I've got two x terms, and I've got two constants. So 5x squared, when I combine my x terms, x minus 3x will be minus 2x. And negative 12 plus 6 will be minus 6. So when I add those polynomials, I have 5x squared minus 2x minus 6. Finally, we want to subtract. But before we subtract, we need to think about opposites. So if I want to know what the opposite of x minus 2 is, which by the way would be written the opposite of the quantity x minus 2, then that means that everything inside here has to be the opposite. So the opposite of x minus 2 would be negative x plus 2. And if I wanted to have the opposite, again, it would look like a negative out front and then my polynomial inside. So if I want to know what the opposite of this polynomial is, I just change the signs on each thing. So it was a negative x squared. Now I'm going to write it as a positive x squared. This was a negative 9x, so I'm going to say plus 9x. This was plus 6, so I will write minus 6. And now I have the opposite coefficient. So that's what we need to do when we're subtracting polynomials. We need to find the opposite of this second polynomial. So I can rewrite this polynomial here. The opposite of 4A minus 8 would be negative 4A plus 8. And then all I have to do is just carry down the rest of my first one, doesn't change at all, so I just carry it down. And since I found the opposite first, I already have my operation in front of my next term. So combining like terms 2A minus 4A plus 4 plus 8, I get negative 2A and 4 plus 8 will give me plus 12. And working on this problem, if I write my first polynomial, I have 5x squared plus x minus 12. Another way to think about this is that you're going to distribute the negative. If I distribute the negative, it's a negative times a negative, which gives me a positive 3x. And then the other way to think is what's the opposite of negative 3x? Positive 3x. And if I go back to my distributive, you have to remember to distribute all the way through. That's why this is my least favorite way to do it. So a negative times a positive is going to give me a negative 6. But what's the opposite of 6? Negative 6. And if you can just remember to take the opposite of your polynomial, then you will take care of all the terms. All right, combining like terms now, I have 5x squared plus x plus 3x, and then I got my minus 12 minus 6. So 5x squared is the only x squared term. And then I've got 2x terms. 1x plus 3 more x's would be plus 4x. And I've got 2 constants here. Negative 12 minus 6 will be minus 18.