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

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Multiply polynomials

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Q. Find the product. Simplify your answer.

\newline

-4a^2(a^2 - 3a)

Identify Expression: Identify the expression after using the distributive property. $\newline$ Distribute $-4a^2$ to $a^2$ and $-3a$ . $\newline$ $-4a^2(a^2 - 3a) = -4a^2(a^2) - 4a^2(-3a)$
Distribute $-4a^2$ : Simplify $-4a^2(a^2)$ . $\newline$ Multiply $-4a^2$ and $a^2$ . $\newline$ $-4a^2(a^2) = -4a^4$
Simplify $-4a^2(a^2)$ : Simplify $-4a^2(-3a)$ . Multiply $-4a^2$ and $-3a$ . $-4a^2(-3a) = 12a^3$
Simplify $-4a^2(-3a)$ : Combine the results from Step $2$ and Step $3$ . $\newline$ We found: $\newline$ $-4a^2(a^2) = -4a^4$ $\newline$ $-4a^2(-3a) = 12a^3$ $\newline$ Now, combine these to get the simplified form of $-4a^2(a^2 - 3a)$ : $\newline$ $-4a^2(a^2 - 3a) = -4a^4 + 12a^3$

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