In Exercises 9–22, multiply the monomial and the polynomial.−4xⁿ ...

Question

In Exercises 9–22, multiply the monomial and the polynomial.−4xⁿ (3x²ⁿ − 5xⁿ + 1/2 x)

Accepted Answer

Hello, everyone. We are gonna perform multiplication for the given monos. We are given negative six X raised the nth power multiplied by the parentheses. Two X raised to the two nth power minus six X raised to the nth power plus one third X closed parentheses. Our answer choices are a 12 XX raised to the three nth power plus 36 X raised to the two nth power minus two X raised to the N plus one power B negative 12 X raised to the three N power plus 36 X raised to the two nth power minus two X raised to the N plus one power C negative X raised to the three N power plus 36 X raised the two nth power plus two X raised the N plus one power D negative 12 X raised to the three N power plus 36 X raised to the two nth power minus two X raised to the N minus one power going back to my given multiplication. I have negative six X raised the nth power open parentheses. Two X raise the two nth power minus six X raise the NTH power plus 1 3rd x closed parentheses. I recall that when I have a mono meal outside a set of parentheses. And I'm asked to multiply that I want to distribute that mono meal into the parentheses. Making sure each term inside the parentheses is multiplied by the mono meal. So I'm gonna start by multiplying negative six X raised to the NTH power by two X raise to the two nth power. Recall. The first thing you wanna do is multiply the coefficients. So negative six multiplied by T two is negative X raised the nth power multiplied by X raised the 2 Nth power. I recall that when I multiply like bases, I add my exponents. So I get X raised to the three nth power. Next I do negative six X raise to the nth power multiplied by negative six X raise to the nth power. -6 multiplied by -6 is a positive X to the nth power multiplied by X to the nth power will give me X to the two nth power because again, I will add my exponents when I multiply like bases. Finally, I will do negative six X rays to the nth power multiplied by one third, X -6, multiplied by 1/3 is -2. Then X raised the nth power multiplied by X. When I combine those, I'll still have the base of X, but I can't add N and one and combine them. So it will just be the N plus one as my exponent Because N&1 are not like terms. So when I'm done distributing what I have is negative 12 XX raised to the three nth power plus 36 X, raise the two nth power minus two X raised to the N plus one power. And that is answer choice B have a nice day.

In Exercises 9–22, multiply the monomial and the polynomial.−4xⁿ (3x²ⁿ − 5xⁿ + 1/2 x)

Key Concepts

Monomials

Polynomials

Distributive Property

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