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Find the product. Simplify your answer. $\newline$ $4r^2(-r^2 - 8)$

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Multiply a polynomial by a monomial

Full solution

Q. Find the product. Simplify your answer.

\newline

4r^2(-r^2 - 8)

Distribute $4r^2$ : Distribute $4r^2$ to both terms inside the parentheses. $\newline$ $4r^2(-r^2 - 8) = 4r^2(-r^2) + 4r^2(-8)$
Simplify $-r^2$ : Simplify $4r^2(-r^2)$ . $4r^2(-r^2) = 4 \times (-r^2) \times r^2 = -4r^4$
Simplify $-8$ : Simplify $4r^2(-8)$ . $4r^2(-8) = 4 \times (-8) \times r^2 = -32r^2$
Combine results: Combine the results from Step $2$ and Step $3$ . $4r^2(-r^2 - 8) = -4r^4 - 32r^2$

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