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# Subtracting polynomials: two variables

Video transcript

We've got 4x squared
y minus 3xy plus 25 minus the entire expression 9y
squared x plus 7xy minus 20. So when we're subtracting
this entire expression, that's equivalent to
subtracting each of these terms individually if we didn't
have the parentheses. Or another way of
thinking about it-- we could distribute
this negative sign. Or you could view this
as a negative 1 times this entire expression. And we can distribute it. So let's do that. So let me write this
first expression here. I'm going to write it unchanged. So it is 4x squared
y minus 3xy plus 25. And now let me distribute
the negative 1, or the negative sign
times all of this stuff. So negative 1 times 9y squared
x is negative 9y squared x. Negative 1 times
7xy is negative 7xy. And then negative 1
times 20 is positive 20. And now we just have
to add these terms. And we just want to
group like terms. So let's see, is there another
x squared y term anywhere? No, I don't see one. So I'll just rewrite this. So we have 4x squared y. Now, is there another xy term? Yeah, there is. So we can group negative
3xy and negative 7xy. Negative 3 of something minus
another 7 of that something is going to be negative
10 of that something. So it's negative 10xy. And then we have a 25, which
is just a constant term. Or an x to the 0 term. It's 25x to the 0. You could view it that way. And there's another constant
term right over here. We can always add 25 to 20. That gives us 45. And then we have this
term right over here, which clearly can't be
merged with anything else. So minus 9y squared. Let me do that in
that original color. Minus 9-- I'm having
trouble shifting colors-- minus 9y squared x. And we are done.