Adding and subtracting polynomials of degree one

0:00- [Instructor] Let's say that A is equal to 6m - 4n - 7p. And let's also say that B is equal to 7m - 3n + 5p. What I wanna do in this video is figure out what is A + B equal to, and I wanna express that in terms of Ms, Ns and Ps. And I want to use as few terms as possible.

0:37So why don't you pause this video and see if you can work through that on your own before we work through it together. All right, now let's work through this together. So first we have A, and I'm just going to rewrite it over here. So we have 6m - 4n - 7p, and then to that we are going to add B, right over here, which is 7m - 3n + 5p.

1:10So what we can do is add the terms that are using the same variables. So for example, I could add the 6m to this 7m, if I have 6ms, and then I add another 7ms, well I'm going to have 13ms here, so that's 13m. And then next I could think about adding, you might wanna say 4n and 3n, but since we're subtracting four and we're subtracting, or we're subtracting 4n, we're subtracting 3n here, you could view it as negative 4n plus negative 3n.

1:44Or you could say we're starting at negative 4n, and then we're subtracting three more ns. Well, negative four minus three is negative seven, so you're now going to have negative seven Ns. Or you could say we're subtracting seven N. And then last but not least, we have, we could say negative 7p and then we are going to add 5p to that.

2:09So if you start at negative 7p and then add 5p, you're gonna get to negative 2p. Another way you could think about it, you have 5p and we're subtracting 7p from that, you're now going to have negative 2p, and we're done. This is, you can't combine any of these, 'cause this is in terms of M, this is in terms of N, and this is in terms of 2p.

2:33Let's do another example here. So, and this one, let's do some subtraction. Let's imagine that we have the expression, or we do have the expression (4x - z) - (8x - 4y + 3z). See if you can do this subtraction. We're subtracting expression from this expression over here.

3:03Pause this video and see if you can do that. All right, now let's work through this together. So the way that I like to do this is essentially distribute this negative sign. You could view this as negative one times all of this. And now to get remove the parentheses, I can just multiply negative one times each of those terms.

3:25So let's do that. So this first part over here, that is just 4x - z. And now let's add, so plus, and I'm going to distribute this negative one onto each of these terms. So we have negative one times 8x, alright, negative 8x. And then we have negative one times negative 4y.

3:50Well that's going to be positive 4y. And then we have negative one times positive 3z. That would be negative 3z. And now we can add terms that are dealing with the same variable. So we can look at this 4x and then we have a negative 8x. So what's 4x plus negative 8x?

4:12Well that's going to be negative 4x. And then we could go to, actually, lemme go to Y next 'cause my brain wants to go from X, to Y, to Z, I could have done Z first, but there's no Y over here and we just have a 4y over here. So I'll just rewrite that plus 4y.

4:31And then last but not least, we have a negative Z here, we're subtracting Z. And now we're subtracting three more Zs right over here. So in total we're going to subtract, we're subtracting a Z and then subtracting three more Zs. We're gonna subtract four Zs. So minus 4z.

4:47And we are done.