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Find the product. Simplify your answer. $\newline$ $-4f(4f^2 - 1)$

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Multiply a polynomial by a monomial

Full solution

Q. Find the product. Simplify your answer.

\newline

-4f(4f^2 - 1)

Distribute $-4f$ : We need to distribute $-4f$ to both terms inside the parentheses: $4f^2$ and $-1$ . $\newline$ $-4f(4f^2 - 1) = -4f \times 4f^2 - 4f \times (-1)$
Simplify $-4f \times 4f^2$ : Now, we simplify $-4f \times 4f^2$ . $-4f \times 4f^2 = -16f^3$ (Multiplying the coefficients and adding the exponents of $f$ )
Simplify $-4f \times (-1)$ : Next, we simplify $-4f \times (-1)$ . $\newline$ $-4f \times (-1) = 4f$ (Multiplying the coefficients and considering the negative signs cancel each other out)
Combine simplified terms: Combine the two simplified terms to get the final answer. $\newline$ $-16f^3 + 4f$

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