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Find the product. Simplify your answer. $\newline$ $-2m^2(-3m^2 - 2m - 1)$

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Multiply polynomials

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Q. Find the product. Simplify your answer.

\newline

-2m^2(-3m^2 - 2m - 1)

Distribute $-2m^2$ : Distribute $-2m^2$ across each term in the trinomial $(-3m^2 - 2m - 1)$ . We need to multiply $-2m^2$ by each term inside the parentheses: $-3m^2$ , $-2m$ , and $-1$ . $-2m^2 \times -3m^2 = 6m^4$ (since $-2 \times -3 = 6$ and $m^2 \times m^2 = m^{2+2} = m^4$ ) $-2m^2$ $0$ (since $-2m^2$ $1$ and $-2m^2$ $2$ ) $-2m^2$ $3$ (since $-2m^2$ $4$ and $-2m^2$ $5$ remains unchanged)
Combine results and simplify: Combine the results from Step $1$ to write the simplified form of the product. $\newline$ The product of $-2m^2$ and $(-3m^2 - 2m - 1)$ is the sum of the individual products: $\newline$ $6m^4 + 4m^3 + 2m^2$

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