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.

(x²ⁿ + 5xⁿ − 8) + (4x²ⁿ − 7xⁿ + 2)

Accepted Answer

Hello, everyone. We have been asked to perform addition in the given expression. And we need to let N represent a whole number. The expression we were given is open parentheses. Five X raised the two N power plus three X raised to the end. Power minus 12 closed parentheses plus open parentheses. Two X raised the two N power minus 11 X raised to the end power plus 21 closed parentheses. Our answer choices are A seven X raised to the two N power minus eight X raised to the N power minus nine B seven X raised to the two N power minus eight X raised to the N power plus nine C seven X raised the two N power minus 14 X raised the N power plus nine D seven X raised the two N power plus eight X raised the N power plus nine. Since there's a plus sign between my two sets of parentheses, I'm going to drop the parentheses as there's no signs that will change. And then I'm gonna combine my like terms. So rewriting this expression without parentheses, I have five X raised the two N power plus three X raised the N power minus plus two X raised the two N power -11 X raised to the end power plus 21. Now, I can combine like terms recall that like terms have the same variable with the same exponent. And just because our exponents aren't the numbers you're used to. This still works. Nothing changes. So for example, we want to start with the highest exponent and work our way down. Our highest exponent here is two N. So we are going to combine the terms that have X raised to the two N power first. So we have five X rays to the two end power and two X rays to the two end power. When we add and combine our leg terms, we just combine our coefficients. So this is seven X raise the two N power. Nothing about that exponent changes. I'm going to cross those out of my rewrite. So I know I've already used them. Next, I'm gonna look for X raised to the end power terms. So I have a positive three X raised to the nth power and a negative 11 X raised to the nth power. When I combine three and negative 11, I get negative eight and X raised the end power is just there. It just comes along with it. Cross those out because again, when we combine our like terms, our exponents on our variables do not change negative 12 and 21 are constants and that's what's left negative 12 plus 21 is a positive nine. So now that I've done my edition combined, all my like terms, my expression is seven X raise to the two nth power minus eight X raise to the NTH power plus nine. That's our solution. And it's answer choice B have a nice day.

In Exercises 29–40, add the polynomials. Assume that all variable exponents represent whole numbers. (x²ⁿ + 5xⁿ − 8) + (4x²ⁿ − 7xⁿ + 2)

Key Concepts

Polynomials

Like Terms

Combining Polynomials

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