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# Adding polynomials: two variables

Sal simplifies (4x²y - 3x² - 2y) + (8xy - 3x² + 2x²y + 4). Created by Sal Khan.

Video transcript

So let's get some practice
simplifying polynomials, especially in the
case where we have more than one
variable over here. So I have 4x squared y
minus 3x squared minus 2y. So that entire expression
plus the entire expression 8xy minus 3x squared
plus 2x squared y plus 4. So the first thing
that jumps out at me is that I'm just adding this
expression to this expression. So to a large degree, these
parentheses don't matter. So I can just rewrite it as
4x squared y minus 3x squared minus 2y plus 8xy minus
3x squared plus 2x squared y plus 4. Now we can try to group
similar terms or like terms. So let's think about
what we have over here. So this first term right
here is a 4x squared y. So can I add this to any
of the other terms here? Do we have any other
x squared y terms? Well, sure, this
one right over here is another x squared y term. If I have 4 of
something-- in this case, I have 4x squared y's and
I add 2x squared y's to it, how many x squared
y's do I now have? Well, 4 plus 2-- I now
have 6x squared y's. Now let's move on to this term. So I have negative 3x squareds. Do I have any more x
squareds in this expression right over here? Well, sure, I have another
negative 3x squared. So if I have negative
3 of something and then I have another negative
3, I end up with negative 6 of that thing. So it's negative 6x squared. Now let's think about
this negative 2y term. Are there any other
y's over here? Well, it doesn't
look like there are. This is an 8xy. This is a 4. There's no just y's. So I can't really
add that to anything. So I'll just rewrite
it, negative 2y. And then 8xy--
well, once again, it doesn't seem like that can
be added to anything else. So let's just write
that over again. And then finally, we just
have the constant term plus 4. And it pretty much
looks like we're done. We have simplified
this as much as we can.