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## Combining like terms

# Combining like terms with negative coefficients & distribution

CCSS.Math:

## Video transcript

I've gotten feedback
that all the Chuck Norris imagery in the last video might
have been a little bit too overwhelming. So for this video, I've included
something a little bit more soothing. Let's try to simplify
some more expressions. And we'll see we're
just applying ideas that we already knew about. Let's say I want to simplify the
expression 2 times 3x plus 5. Well, this literally
means two 3x plus 5's. So this is the exact same thing. This is one 3x plus
5, and then to that, I'm going to add
another 3x plus 5. This is literally what
2 times 3x plus 5 means. Well, this is the same thing
as, if we just look at it right over here, we have now two 3x's. So we could write
it as 2 times 3x. Plus, we have two 5's,
so plus 2 times 5. You might say, hey, Sal, isn't
this just the distributive property that I know
from arithmetic? I've essentially just
distributed the 2? 2 times 3x plus 2 times 5? And I would tell
you, yes, it is. And the whole reason why I'm
doing this is just to show you that it is exactly
what you already know. But with that out of the way,
let's continue to simplify it. When you multiply the 2
times the 3x, you get 6x. When you multiply the 2
times the 5, you get 10. So this simplified
to 6x plus 10. Now let's try something that's
a little bit more involved. Once again, really just
things that you already know. Let's say I had 7 times 3y minus
5 minus 2 times 10 plus 4y. Let's see if we
can simplify this. Well, let's work on
the left-hand side of the expression, the
7 times 3y minus 5. We just have to
distribute the 7. This is going to be 7 times 3y,
which is going to give us 21y. Or if I had 3 y's
7 times, that's going to be 21 y's, either way
you want to think about it. And then I have 7
times-- we've got to be careful with
the sign-- negative 5. 7 times negative
5 is negative 35. So we've simplified
this part of it. Let's simplify the
right-hand side. You might be tempted to say,
oh, 2 times 10 and 2 times 4y and then subtract them. And if you do that right and
you distribute the subtraction, it would work out. But I like think of
this as negative 2, and we're going to
distribute the negative 2 times 10 and the
negative 2 times 4y. So negative 2 times
10 is negative 20, so it's minus 20
right over here. And then negative 2 times
4, negative 2 times 4 is negative 8, so it's
going to be negative 8y. Let's write a minus
8y right over here. And are we done simplifying? Well, no, there's a little
bit more that we can do. We can't add the 21y to the
negative 35 or the negative 20 because these are
adding different things or subtracting different things. But we do have two things
that are multiplying y. Let me do all in
this green color. You have 21 y's right over here. And then we can view it as from
that we are subtracting 8 y's. So if I have 21 of something
and I take 8 of them away, I'm left with 13
of that something. So those are going to
simplify to 13 y's. I'll do this in a new color. And then I have
negative 35 minus 20. That's just going to
simplify to negative 55. So this whole thing
simplified, using a little bit of the distributive
property and combining similar or like terms,
we got to 13y minus 55.