Adding & subtracting polynomials: two variables
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.