Subtract −4x³ − x²y + xy² + 3y³ from x³ + 2x²y − y³.

Question

Accepted Answer

Hey, everyone. In this problem, we're asked to perform subtraction as indicated negative five X cubed minus five X squared, Y plus two X Y squared plus seven Y cubed from two X cubed minus three X squared, Y plus two X Y squared plus three Y cubed. We're given four answer choices. Option A seven X cubed plus two X squared, Y minus four Y cubed. Option B seven X Q minus two X squared, Y -4 YQ option C seven X Q plus two X squared, Y plus four Y Q and option D seven X cubed minus two X squared, Y plus four Y cubed. Now we're gonna start by just writing what we were given in the problem text in terms of the math. OK. So we want to perform subtraction. We wanna subtract the first expression given from the second expression given. So we have the second expression two X cubed minus three X squared, Y plus two X Y squared Plus 3 YQ. We're gonna subtract from this expression negative five X cubed minus five X squared, Y plus two X Y squared plus seven Y cubed. So this is the subtraction that we're asked to perform. We wanna go ahead and simplify this big expression that we have. The first thing we wanna do is get rid of these brackets. So we just have one great big long expression. OK. The first expression, we can remove the brackets. There's nothing kind of acting on those brackets. For the second half of our expression, we have minus this great big expression. So we need to distribute that minus to every single term inside of the brackets. And we're subtracting every single one of those terms. So where we have a negative, OK, we're subtracting a negative value that's gonna become a positive. OK? A negative multiplied by a negative gives us a positive where we have a positive value, subtracting a positive value that's gonna be a negative value. OK? We're gonna continue to subtract. So if we apply that, we have two X cubed minus three X squared, Y plus two X Y squared plus 3 y cubed plus 5 x cubed plus five X squared, Y minus two X Y squared -7 YQ. Now we have the brackets gone. We've expanded this expression as much as possible and we're left with just collecting like terms, OK? In order to simplify, that's what we're gonna do. We're gonna collect like terms. Let's start on the left hand side and just work our way over. We have a two X cube term here. So we're gonna look and see if there are any other X cube terms, we also have plus 5 x cubed. So we have two X cubed plus five X cubed. This gives us seven X cubed in our resulting expression. Moving to the next term we have minus three X squared Y. And we want to look for other X squared Y terms. And later on in our equation, we add five X squared Y so negative three X squared Y plus five X squared Y gives us plus two X squared Y in our resulting expression continuing on. The next term in our expression is two X Y squared. So we wanna look for other X Y squared terms. Well, we have a negative two X Y squared term. So two X Y squared minus two X Y squared, that's gonna give us just zero. Yeah. So those two terms add to zero and then we have the final two terms, 3 y cubed minus seven Y cubed. This gives us minus four Y cubed. And that's as simple as we can get it. We combined all of those like terms. And that's the result we were looking for from the subtraction. If we compare this to our answer choices, we found the result with seven X cubed plus two X squared, Y minus four Y cubed which corresponds with answer choice. A thanks everyone for watching. I hope this video helped see you in the next one.

Subtract −4x³ − x²y + xy² + 3y³ from x³ + 2x²y − y³.

Key Concepts

Polynomial Subtraction

Like Terms

Combining Polynomials

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