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## Combining like terms

Current time:0:00Total duration:3:43

## Video transcript

We have a hairy-looking
expression here. And your goal is to try to
simplify it as much as you can. And I'll give you a little
bit of time to do it. Let's just think about
it, step by step. And it might help if we
were to actually reorder the terms in this expression. So let me put all
the x terms first. So I have 5x-- that's
that term-- minus 2x. Then I have plus 7y plus 3y. Then i have plus 8z,
and then I have minus z. And then the last term
that I haven't included yet is that plus 5. Now we'll just think it through. If I have 5 x's and
I were to take away 2 x's, is how many x's am
I going to be left with? Well, I'm going to
be left with 3 x's. That's true of anything. There's not some fancy
algebraic magic going on here. 5 of anything minus
2 of that same thing, you're going to be left
with 3 of that thing. In this case, that
thing are x's. So this is going
to simplify to 3x. Now, in a lot of
algebra classes, you'll hear people say,
oh, well, you know, the coefficient on 5x is 5. And the coefficient on
this subtracting the 2x, the coefficient
here is negative 2, and we had to add
the coefficients. Let me write that word
down-- coefficient. These right over here
are the coefficients. They're the number that you're
multiplying the variable by. So you're the 5 or the
negative 2 in this case. And so you could
just say, oh, I had to just add the coefficients. And that's OK, and there's
nothing wrong with that. But I really want to
emphasize that there's a very common sense
intuition here. If you have 5 of something, you
take away 2 of that something, you are left with 3
of that something. And you have to be very careful. You have to make sure that
you're adding and subtracting the same things. Here, we're dealing with x's. So we can take 5 x's
and take away 2 x's. We can't think about merging
the x's and the y's, at least not in any simple way right
now, because that, frankly, wouldn't make any
intuitive sense. Now let's think about the y's. If I have 7 of something,
and I were to add 3 more of that something,
well, then, I'm going to have 10
of that something. So this part right over here
is going to simplify to 10y. Once again, you could say
the coefficient on 7y is 7. The coefficient on 3y is 3. We added the coefficients--
7 plus 3-- to get 10y. But I really want to
emphasize the intuition here. It's much more if you've got 7
of something, you add another 3 to that something, you've
got 10 of that something. Now let's look at the z's. If I've got 8 of something
and I take away 1 of them, I'm going to have 7
of that something. So that is 7z. And you might say, hey, wait. What was the coefficient
right here on this negative z? I don't see any number
out front of the z. Well, implicitly, I
could have put a 1 here, and it's exactly the same thing. Subtracting a z is the exact
same thing as subtracting 1z. The word "onesie" strikes
a part of my brain because I have very
young children, but that's a different
type of onesie. And then you could
see, oh, yeah, you definitely did add the
two coefficients, the 8 and the negative 1. But once again,
common sense tells you if you have 8 of something,
and you take away 1 of them, you have 7 of that something. And then finally,
you have a plus 5. So we're done. This simplified to 3x
plus 10y plus 7z plus 5.