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Find the product. Simplify your answer. $\newline$ $-3f^2(-3f^2 + 4f)$

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Multiply polynomials

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Q. Find the product. Simplify your answer.

\newline

-3f^2(-3f^2 + 4f)

Distribute $-3f^2$ : Distribute $-3f^2$ to each term inside the parentheses. $\newline$ We need to apply the distributive property $a(b + c) = ab + ac$ . $\newline$ $-3f^2(-3f^2 + 4f) = -3f^2 \cdot -3f^2 + -3f^2 \cdot 4f$
Simplify $-3f^2 \times -3f^2$ : Simplify $-3f^2 \times -3f^2$ . $\newline$ Multiply the coefficients and add the exponents for $f$ . $\newline$ $-3f^2 \times -3f^2 = 9f^4$
Simplify $-3f^2 \times 4f$ : Simplify $-3f^2 \times 4f$ . $\newline$ Multiply the coefficients and add the exponents for $f$ . $\newline$ $-3f^2 \times 4f = -12f^3$
Combine results: Combine the results from Step $2$ and Step $3$ . $\newline$ We have found: $\newline$ $9f^4$ from Step $2$ $\newline$ $-12f^3$ from Step $3$ $\newline$ So, $-3f^2(-3f^2 + 4f) = 9f^4 - 12f^3$

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