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Find the product. Simplify your answer. $\newline$ $-3v^2(v^2 - 9)$ $\newline$ ________

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Multiply a polynomial by a monomial

Full solution

Q. Find the product. Simplify your answer.

\newline

-3v^2(v^2 - 9)

\newline

________

Distribute terms: Distribute $-3v^2$ to $v^2$ and $-9$ . $\newline$ $-3v^2(v^2 - 9) = -3v^2 \times v^2 + -3v^2 \times -9$
Simplify $v^2$ : Simplify $-3v^2 \times v^2$ . $\newline$ $-3v^2 \times v^2 = -3v^4$
Simplify $-9$ : Simplify $-3v^2 \times -9.$ $-3v^2 \times -9 = 27v^2$
Combine terms: Combine the two simplified terms. $-3v^4 + 27v^2$

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