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

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Multiply polynomials

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Q. Find the product. Simplify your answer.

\newline

(4s - 1)(4s^2 + 2s + 4)

Multiply $4$ s with terms: We start by multiplying $4s$ with each term in the second binomial: $\newline$ $4s \times 4s^2 = 16s^3$ $\newline$ $4s \times 2s = 8s^2$ $\newline$ $4s \times 4 = 16s$ $\newline$ So, $4s(4s^2 + 2s + 4) = 16s^3 + 8s^2 + 16s$
Multiply $-1$ with terms: Next, we multiply $-1$ with each term in the second binomial: $\newline$ $-1 \times 4s^2 = -4s^2$ $\newline$ $-1 \times 2s = -2s$ $\newline$ $-1 \times 4 = -4$ $\newline$ So, $-1(4s^2 + 2s + 4) = -4s^2 - 2s - 4$
Combine and simplify: Now, we combine the results from the previous two steps: $\newline$ $(16s^3 + 8s^2 + 16s) + (-4s^2 - 2s - 4)$ $\newline$ We add the like terms to simplify the expression: $\newline$ $16s^3 + (8s^2 - 4s^2) + (16s - 2s) - 4$ $\newline$ $16s^3 + 4s^2 + 14s - 4$

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