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

5x³...

Question

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

5x³ (2x⁵−4x²+9)

Accepted Answer

Hello, everyone. We've been asked to perform multiplication for the given mono meals. We are given eight X cubed multiplied by in parentheses. Six X raised to the fifth power minus nine X squared plus 10. Our answer choices are a 48 X raised to the eighth power minus 72. X raise to the fifth power plus 80 X cubed B 48 X ray to the eighth power minus 72 X ray to the fifth power minus 80 X cubed C 48 X raised to the eighth power plus 72 X raise to the fifth power plus 80 X cubed D 48 X raised to the eighth power plus 72 X raised to the fifth power minus 80 X cubed rewriting what we were given. We have 8 x cubed multiplied by open parentheses. 6 x raise the 5th power minus nine X squared plus 10 closed parentheses to multiply this. I am going to be distributing eight X to the third power into the parentheses. So each term in our parentheses is multiplied by eight X cubed. So first we'll do eight X cubed multiplied by six X rays to the fifth power, we multiply the coefficients first eight multiplied by 6 is 48 X cubed multiplied by X raised to the fifth power. When we multiply like bases, the base stays the same. And we add our exponents three plus five is eight. So our first term is 48 x raise to the 8th power. Next we do eight X cubed multiplied by negative nine X squared. Again, we multiply our coefficients first eight times negative nine is negative 72 X raised to the third power multiplied by X raise to the second power. We keep the X, we add our exponents. So we have X raised to the fifth power. Finally, the last term 8 x cubed multiplied by 10, eight plus uh sorry, eight multiplied by 10 is 80. So plus 80 then X cube doesn't have anyone to change it. So it remains X cubed. So when we put this all together, we have 48 X raised to the eighth power minus 72 X raise to the fifth power plus X cubed. That is our product and our answer choice. A have a nice day.

In Exercises 9–22, multiply the monomial and the polynomial. 5x³ (2x⁵−4x²+9)

Key Concepts

Monomials

Polynomials

Distributive Property

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