Subtracting polynomials: two variables

- [Voiceover] We're asked to subtract negative six X to the fourth minus three X squared Y squared plus Y to the fourth from two X to the fourth minus eight X squared Y squared mins Y to the fourth. And I encourage you to pause this video and give it a try. Alright, let's work through it together. So We're gonna subtract this green polynomial from this magenta one. So we can rewrite this as, we're to actually perform it we could write two X to the fourth minus eight X squared Y squared minus Y to the fourth minus, and I'm gonna write this in parenthesis, give us some space, minus negative six X to the fourth minus three X squared Y squared plus five Y to the fourth. So notice, I'm subtracting this green polynomial in two variables from this magenta polynomial in two variables. Which is exactly what it says to do up here. So what's this going to be? Well I can just rewrite the magenta part. We're gonna have two X to the fourth minus eight X squared Y squared minus Y to the fourth. And then I can distribute this negative sign. So if we say the negative of negative six X to the fourth, that's gonna be positive six X to the fourth. So that's gonna go positive six X to the fourth. And then the negative of negative three X squared Y squared is going to be positive three X squared Y squared. So plus three X squared Y squared. And then last but not least, we have a negative, or we're subtracting positive five Y to the fourth. So that's going to be subtracting five Y to the fourth, or negative five Y to the fourth. And now we can try to simplify. So let's first look at this term right over here. We have two X to the fourths. And what we could look for is another X to the fourth term. And we see it right over here. So we have two X to the fourths and we can add that to six X to the fourths. So what's that going to be? Well if I have two of something, and then I add another six of that something, that's going to be eight X to the fourths, two plus six. Two X to the fourth plus six X to the fourth is going to be eight X to the fourth power. And now we have this X squared Y squared term. We could say we're subtracting eight of them. And over here we're adding three of these X squared Y squared terms. So we could add these coefficients. If we're taking away eight, but we're adding three we could view this as negative eight X squared Y squareds plus three X squared Y squareds. Well what's negative eight plus three? Well that's going to be negative five. Negative five X squareds Y squareds. So that's that term. Let me write that a little bit neater. That's this term right over here, don't forget to include this sign here. This is you're subtracting eight X squared Y squareds, you could do that as negative eight X squared Y squared plus three X squared Y squared. And then last but not least, you're subtracting one Y to the fourth, and then you're subtracting five more Y to the fourths. So what's that going to be? You could view this as negative one Y to the fourth minus five Y to the fourths. Well that's going to be negative one minus five is negative six. Negative six Y to the fourths. And we're done, we have subtracted this from that.