Main content

## Algebra (all content)

### Unit 1: Lesson 8

Combining like terms- Intro to combining like terms
- Combining like terms with negative coefficients & distribution
- Combining like terms with distribution
- Combining like terms with distribution
- Combining like terms with negative coefficients
- Combining like terms with negative coefficients
- Combining like terms with negative coefficients & distribution
- Combining like terms with rational coefficients
- Combining like terms with rational coefficients
- Combining like terms review

© 2022 Khan AcademyTerms of usePrivacy PolicyCookie Notice

# Combining like terms with negative coefficients

CCSS.Math:

This example of combining like terms in an expression get a little hairy. Pay attention. Created by Sal Khan.

## Video transcript

Now we have a very, very,
very hairy expression. And once again, I'm going to
see if you can simplify this. And I'll give you
little time to do it. So this one is even crazier than
the last few we've looked at. We've got y's and
xy's, and x squared and x's, well more just xy's and
y squared and on and on and on. And there will be a temptation,
because you see a y here and a y here to
say, oh, maybe I can add this negative
3y plus this 4xy somehow since I see a y and a y. But the important
thing to realize here is that a y is
different than an xy. Think about it
they were numbers. If y was 3 and an x was a
2, then a y would be a 3 while an xy would have been a 6. And a y is very different
than a y squared. Once again, if the why it
took on the value 3, then the y squared would
be the value 9. So even though you see
the same letter here, they aren't the same-- I
guess you cannot add these two or subtract these two terms. A y is different
than a y squared, is different than an xy. Now with that said, let's
see if there is anything that we can simplify. So first, let's think
about the y terms. So you have a negative 3y there. Do we have any more y term? Yes, we do. We have this 2y
right over there. So I'll just write it
out-- I'll just reorder it. So we have negative 3y plus 2y. Now, let's think
about-- and I'm just going in an arbitrary order,
but since our next term is an xy term-- let's think about
all of the xy terms. So we have plus 4xy
right over here. So let me just write
it down-- I'm just reordering the whole
expression-- plus 4xy. And then I have minus
4xy right over here. Then let's go to
the x squared terms. I have negative 2 times x
squared, or minus 2x squared. So let's look at this. So I have minus 2x squared. Do I have any other x squared? Yes, I do. I have this 3x squared
right over there. So plus 3x squared. And then let's see, I have
an x term right over here, and that actually looks
like the only x term. So that's plus 2x. And then I only
have one y squared term-- I'll circle that in
orange-- so plus y squared. So all I have done is I've
reordered the statement and I've color coded it based
on the type of term we have. And now it should be
a little bit simpler. So let's try it out. If I have negative
3 of something plus 2 of that something,
what do I have? Or another way to say it,
if I have two of something and I subtract 3 of that,
what am I left with? Well, I'm left with negative
1 of that something. So I could write negative 1y, or
I could just write negative y. And another way you
could think about it, but I like to think about
it intuitively more, is what's the coefficient here? It is negative 3. What's the coefficient here? It's 2. Where obviously
both are dealing-- they're both y
terms, not xy terms, not y squared terms, just y. And so negative 3
plus 2 is negative 1, or negative 1y is the
same thing as negative y. So those simplify to
this right over here. Now let's look at the xy terms. If I have 4 of
this, 4 xy's and I were to take away 4 xy's,
how many xy's am I left with? Well, I'm left with no xy's. Or you could say add
the coefficients, 4 plus negative 4,
gives you 0 xy's. Either way, these
two cancel out. If I have 4 of something
and I take away those 4 of that something,
I'm left with none of them. And so I'm left with no xy's. And then I have
right over here-- I could have written
0xy, but that seems unnecessary--
then right over here I have my x squared terms. Negative 2 plus 3 is 1. Or another way of saying
it, if I have 3x squared and I were to take
away 2 of those x squared, so I'm left
with the 1x squared. So this right over here
simplifies to 1x squared. Or I could literally
just write x squared. 1x squared is the same
thing as x squared. So plus x squared,
and then these there's nothing really left to simplify. So plus 2x plus y squared. And we're done. And obviously you
might have gotten an answer in some other
order, but the order in which I write these
terms don't matter. It just matters that you
were able to simplify it to these four terms.