 And welcome back. Today we're going to talk about adding and subtracting polynomials. Actually, this video will be a pretty short video. It's actually pretty trivial to add and subtract polynomials. The general rule here, when you want to add and subtract polynomials, you want to combine like terms. That's another kind of word that you might hear from your instructions or something like that. Technically, this is what we're doing. We're just combining like terms. Combine like terms. The terms have to have the same variable to the same power. Now, what's going to happen is we're going to look at these a couple of examples. And that's basically what we're going to look for. We're going to look for the same variable to the same power. And then those are going to be like terms. Those are the ones we're actually going to combine together. We can't combine everything into one nice, neat little term that doesn't quite work that way. All right, so the first one here, we have two polynomials. We're going to add them together. We have a polynomial over here and a polynomial over here. Now to get into technical terms using a little bit of vocabulary, since it's to the third power and there's three terms, this is a cubic trinomial. And then over here, the highest power is actually over here. So this is actually a cubic term. We call this a cubic polynomial with four terms. We don't have a special name for polynomials above three at this point. So we just call it a polynomial with four terms. But anyway, a lot of students, when they look at a problem like this, they make the mistake that they think they're multiplying. You see parentheses over here. You see parentheses over here. Don't make that mistake. Look at the sign in between. We are simply adding these two polynomials together. The only reason that we have parentheses is to differentiate the difference between our polynomial over here and our polynomial over here. That's it. That's the only reason for those parentheses. All right, so other than that, we can actually kind of, for this problem anyway, we can kind of ignore them. For the next one, we can't really do that and I'll show you why here in a minute. Okay, so what I'm going to do is I'm simply just going to find my like terms and add them together. Notice first, we have an x cubed. So there's one term and then over here we also had the x cubed that I mentioned earlier. Those are my like terms. Those are terms that have the same variable to the same power. They both have x's and they both have cubes. They're both to the third power. So that means those ones are like terms. I can combine them together. Now what do we mean by combining? Combining means adding or subtracting the coefficients. Now again, a little bit of vocab. Coefficients are the numbers in front of the variables. So in this case a two and in this case a three. So I simply just want to add those together. So in this case I'm going to get three x to the third. Notice that the variables didn't change. X's stayed x's, the cube's there, the three stayed three, but it's the coefficients, the numbers out front. That is what's going to change. Okay, now moving on. Now that I've dealt with my to the third powers, now I'm going to go to the second power. So as I scan through this, the only second power I see is this one right here. Now notice I double underlined it. This is a strategy I use to kind of keep track of what I'm adding together. Okay, so this one is just all by its lonesome, so we're just going to rewrite it. Five x squared. Now make sure you get the plus five x squared in there. All right, moving on. Now we go one step lower. So x squared, now we go to our x's. So I see one right here, little three line, and then I see one right here. Okay, so that's a negative one x and a positive seven is going to get a positive six x. Again, the exponents are not going to change. It's only the coefficients. It's only the numbers out front. And then last but not least, I have my constants. I got nine and four, which is going to make 13. Not going to put lines underneath those. And that's it. That is my simplified polynomial. Simplified polynomial, okay? And from there, I'm not going to combine anything else. These are all separate terms. I'm not going to add anything together. They just stay the way that they look right now. Again, to go back into the vocabulary, this is a, my highest power is three, okay? And so this would be a cubic polynomial with four terms. I got one, two, three, four terms. So again, a cubic polynomial. Just use a little bit of vocabulary there. Anyway, the next one, the next one that we have down here, I'm just going to do the same thing. Now, the one thing here you've got to realize is that we are subtracting this polynomial over here to the right. This quadratic, highest power is two quadratic trinomial. Okay, so we're subtracting that, which actually we do need to do one step. First, we need to distribute that negative. So what I'm going to do is I'm right down here, I'm going to rewrite this, three minus two x squared. This one is not going to change. It's only the one on the right, the one that has the negative in front. So take this negative and apply it to everything in your parentheses. Negative x squared minus six plus x. Changed all the signs in there. And now we can do just like what we did above, we can identify what is alike and add those together, okay? Add the coefficients. So what I notice here is my highest powers are actually two's right here. So here's one and here's one. Negative two, and make sure you get these negatives in front. Make sure you get these signs. Okay, negative two and negative one is going to make a negative three x squared. And then going down one step, I have my x's, but I don't have any other x's, so that's guys is all mine is lonesome. And then I have my constants of three and negative six to make a negative three. Okay, then now I've gotten down to a quadratic trinomial is what I have left over. Alrighty, that's adding and subtracting polynomials relatively quick and simple. Again, the one thing I want to remember, when you are combining like terms, the terms have to be to the same variable to the same power. Same variable, same power. You add or subtract the coefficients the numbers out front. That's the basics behind adding and subtracting polynomials. All right, I hope you enjoyed the video and we'll see you next time.