In Exercises 41–50, subtract the polynomials. Assume that all var...

Question

In Exercises 41–50, subtract the polynomials. Assume that all variable exponents represent whole numbers.

(x³ + 7xy − 5y²) − (6x³ − xy + 4y²)

Accepted Answer

Mhm Hey, everyone in this problem, we're asked to perform subtraction in the given expression. And the expression we have is X cubed plus 12 X Y minus 17 Y squared minus seven brackets five X cube minus three, X Y plus eight Y squared. We're given four answer choices. Option A negative four, X Q plus 15 X Y minus 25 Y squared. Option B negative six X cubed plus nine X Y minus 25 Y squared. Option C negative four X Q plus 15 X Y plus 25 Y squared. In option D six X cubed plus nine X Y minus 25 Y squared. We're gonna start by rewriting the expression. We were given X cubed plus 12 X Y minus 17 Y squared minus and in brackets five X cubed minus three X Y plus eight Y squared. The first thing we wanna do is to go ahead and get rid of these brackets. Now, in order to get rid of the brackets, we have this minus sign in the middle, which applies to everything in the bracket behind it. And so we need to distribute that minus to each term in the bracket. All right. So the first brackets, those are just, we can get rid of those. No problem. There's no negative applied, there's no coefficient, it's not being multiplied. So we have X cubed plus 12 X Y -17 Y Squared. And then we have negative five X cubed, we're gonna have minus five X cubed minus negative three X Y negative terms and negative gives us a positive. So we have plus three X Y, then we have negative eight Y squared. And so we subtract eight Y squared. And now we've gotten rid of those brackets completely. We have one big expression. It's been simplified and now we want to combine like terms. So combining my terms, we have an X cube term, we have a -5 XQ term. So combining those, we have X cubed minus five X cubed, we're gonna add our next term. Our next term we have is 12 XY. We also have a three X Y term. So we have 12 X Y plus three X Y. OK. If we're looking at combining light terms, we have a negative 17 Y squared term and a negative 8 y square term. We have plus negative 17 Ys word -8 Y Squared. And that takes care of all of the terms in our expression. And now we can just simplify these collected like terms. So X cube minus five X cube, this gives us negative or X cube. We have 12 X Y plus three X Y which gives us 15 X Y and we have negative 17 Y square minus eight Y square, which gives us negative 25 Y square. And so we subtract 25 Y squared. And that's our simplified expression. We've done subtraction. We simplified as much as we can. And that was the result we were hoping for. If we compare this to our answer choices, this corresponds with answer choice. A negative four X cubed plus 15 X Y minus 25 Y squared. Thanks everyone for watching. I hope this video helped see you in the next one.

In Exercises 41–50, subtract the polynomials. Assume that all variable exponents represent whole numbers. (x³ + 7xy − 5y²) − (6x³ − xy + 4y²)

Key Concepts

Polynomial Subtraction

Like Terms

Exponents and Variables

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