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

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Multiply a polynomial by a monomial

Full solution

Q. Find the product. Simplify your answer.

\newline

2d^2(2d^2 - d)

Distribute $2d^2$ : Distribute $2d^2$ to both terms inside the parentheses. $\newline$ $2d^2(2d^2 - d) = 2d^2 \times 2d^2 - 2d^2 \times d$
Simplify $2d^2 \times 2d^2$ : Simplify $2d^2 \times 2d^2$ . $\newline$ $2d^2 \times 2d^2 = 4d^{(2+2)} = 4d^4$
Simplify $2d^2 \cdot d$ : Simplify $2d^2 \cdot d$ . $2d^2 \cdot d = 2d^{(2+1)} = 2d^3$
Combine simplified terms: Combine the simplified terms. $2d^2(2d^2 - d) = 4d^4 - 2d^3$

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