Find the product. Simplify your answer. -3d(-d^2 + 7) ______

Distribute -3d: Distribute -3d to both terms inside the parentheses. -3d(-d^2 + 7) = -3d * -d^2 + -3d * 7Simplify -3d * -d^2: Simplify -3d * -d^2. -3d * -d^2 = 3d^3 (Multiplying two negatives gives a positive, and d multiplied by d^2 gives d^3)Simplify -3d * 7: Simplify -3d * 7. -3d * 7 = -21d (Multiplying a negative by a positive gives a negative)Combine results: Combine the results from Step 2 and Step 3. The simplified form of -3d(-d^2 + 7) is 3d^3 - 21d.

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Find the product. Simplify your answer. $\newline$ $-3d(-d^2 + 7)$

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Math Problems

Algebra 1

Multiply a polynomial by a monomial

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Q. Find the product. Simplify your answer.

\newline

-3d(-d^2 + 7)

Distribute $-3d$ : Distribute $-3d$ to both terms inside the parentheses. $\newline$ $-3d(-d^2 + 7) = -3d \cdot -d^2 + -3d \cdot 7$
Simplify $-3d \times -d^2$ : Simplify $-3d \times -d^2$ . $\newline$ $-3d \times -d^2 = 3d^3$ (Multiplying two negatives gives a positive, and $d$ multiplied by $d^2$ gives $d^3$ )
Simplify $-3d \times 7$ : Simplify $-3d \times 7$ . $\newline$ $-3d \times 7 = -21d$ (Multiplying a negative by a positive gives a negative)
Combine results: Combine the results from Step $2$ and Step $3$ . $\newline$ The simplified form of $-3d(-d^2 + 7)$ is $3d^3 - 21d$ .