Subtracting polynomials: two variables (intro)

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.