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Find the product. Simplify your answer. $\newline$ $m^2(-m^2 + 7)$

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Multiply a polynomial by a monomial

Full solution

Q. Find the product. Simplify your answer.

\newline

m^2(-m^2 + 7)

Distribute $m^2$ : Distribute $m^2$ to both terms inside the parentheses. $\newline$ $m^2(-m^2 + 7) = m^2(-m^2) + m^2(7)$
Simplify $-m^2$ : Simplify $m^2(-m^2)$ . $m^2(-m^2) = -m^{2+2} = -m^4$
Simplify $7m^2$ : Simplify $m^2(7)$ . $m^2(7) = 7m^2$
Combine terms: Combine the simplified terms to get the final answer. $\newline$ $m^2(-m^2 + 7) = -m^4 + 7m^2$

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