In Exercises 29–40, add the polynomials. Assume that all variable...

Question

In Exercises 29–40, add the polynomials. Assume that all variable exponents represent whole numbers.

(9x⁴y² − 6x²y² + 3xy) + (−18x⁴y² − 5x²y − xy)

Accepted Answer

Hello, everyone. We are going to perform edition. In the given expression. The expression we're given is open parentheses. 11 X raise to the fourth power Y squared minus seven X squared, Y squared plus six X Y closed parentheses plus open parentheses. Negative 24 X raised to the fourth power Y squared minus 13, X squared, Y minus four X Y closed parentheses. Our answer choices are a X raise the fourth power Y squared minus seven X squared, Y squared minus 13 X squared, Y plus two X Y B 13 X raised the fourth power Y squared minus seven X squared, Y squared minus 13 X squared, Y plus two X Y C negative 13 X raise the fourth power Y squared minus seven X squared, Y squared minus 13 X squared, Y plus two X Y D negative 13 X raised to the fourth power Y squared minus seven X squared, Y squared minus 13 X squared, Y minus two X Y. Going back to my original expression, I'm going to rewrite this expression without parentheses. The reason I'm gonna drop the parentheses is because there's a plus sign in between the two sets of parentheses, which means I'm just gonna be combining my like terms. So we have 11 X raised to the fourth power Y squared minus seven X squared, Y squared plus six X Y plus negative 24 X raised the 4th power y squared minus 13 X squared Y -4 XY. So now I'm going to combine my like terms. Recall that like terms have the same variables with the same exponents if they don't match exactly, we cannot combine them. We also start with our highest exponents and work our way down. So the highest exponents here would be X rays to the 4th power y squared. So those are the terms I'm gonna combine. First, I have an 11 X raised the fourth power Y squared and a negative 24 X raised the fourth power Y squared. When I combine like terms, I combine my coefficients and my exponents and variables stay the same. So 11 plus negative 24 is negative X raised to the 4th power y squared. And now that I've used that term, I'm crossing it out of my original terms. So that way I don't have to look at it again. I don't accidentally mess it up. Next, I would look to see if I had anything with X rays to the third power I do not. So next, I'm gonna go X squared. So I have an X squared, Y squared term and an X squared. Y X squared, Y squared is considered a higher power. So we're gonna do that. Next, there's only one of those. So negative seven X squared Y squared is my next term and I'm gonna cross it out of my original terms. Again, after that, I will go to my negative 13 X squared Y and there's no like term for that. So again, minus 13 X squared Y is my next term crossing it out. Finally, I'm left with X Y terms. So I have a six X Y and a negative four X Y six plus negative four is a positive two X Y. So our answer is negative 13 X raised to the fourth power Y squared minus seven X squared, Y squared minus 13 X squared Y plus two X Y. And that is answer choice C have a nice day.

In Exercises 29–40, add the polynomials. Assume that all variable exponents represent whole numbers. (9x⁴y² − 6x²y² + 3xy) + (−18x⁴y² − 5x²y − xy)

Key Concepts

Polynomials

Like Terms

Combining Polynomials

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