Perform the indicated operations. Indicate the degree of the resu...

Question

Perform the indicated operations. Indicate the degree of the resulting polynomial. (13x^3y^2-5x^2y-9x^2)-(-11x^3y^2-6x^2y+3x^2-4)

Accepted Answer

Welcome back. I'm so glad you're here. We are performing the indicated operation indicated operation here is subtraction. So we're subtracting these two rude polynomial and then we're going to find the degree of that resulting polynomial. So first let's start by subtracting and step one is going to be that. We're going to carefully copy that because there's a lot of terms going on. Two X cubed, Y squared minus nine X squared Y plus 11, X squared minus new parentheses, negative X cubed y squared minus eight X squared y plus seven X squared minus four. And the second thing we want to be very careful is when we're distributing this negative to all four terms in the second set of parentheses and I'm going to make a note for myself what those sign changes are going to be So a negative times a negative. The first term is going to be a positive negative times negative for the second term is going to be positive negative times a positive for the third term is going to be negative negative times a negative for the fourth term is going to be positive. So now we can drop the parentheses in the first set and bring this down to X cubed y squared minus nine X squared y plus 11 X squared plus x cubed y squared plus eight, X squared y minus seven X squared and plus four. Great. We've got that down And now we want to find like terms. So let's start with our X cubed Y squared. We've got two of them plus another one of them. Two plus one is three. So now we have three X cubed Y squared. Let's look at our next terms. We've got this negative nine X squared Y plus eight more X squared Y. That's going to be minus one or just minus X squared Y. We'll look at our next one. We've got 11 X squared minus seven X squared. So that's going to leave us with positive four X squared. And then we don't want to forget our friend plus four here on the end. So we've got the first part done great. And now let's look at the degree of the resulting polynomial to find the degree. We look at the degree of each of these four terms. The first term has three for the X and two for the Y. We add those together. So that's got a degree of five for the first term. The second term has degree of two and then there's an invisible one here for that Y. So we add those together and it's got a degree of three. This third term has a degree of two and this fourth term it has a degree of zero because it's being multiplied by X to the zero which is one. So four times one is four and it's got a degree of zero. We take the highest degree out of those four terms degrees and that's going to be five. So the degree of the entire resulting polynomial the entire polynomial is five. We look at our answer choices and that matches with answer choice a well done, we'll catch you on the next one.

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