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Find the product. Simplify your answer. $\newline$ $(w - 2)(3w^2 - 4w + 1)$

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Multiply polynomials

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Q. Find the product. Simplify your answer.

\newline

(w - 2)(3w^2 - 4w + 1)

Distribute and Multiply: Distribute each term in the first polynomial $(w - 2)$ to each term in the second polynomial $(3w^2 - 4w + 1)$ . We will first multiply $w$ by each term in the second polynomial, then multiply $-2$ by each term in the second polynomial.
Multiply $w$ by Polynomial: Multiply $w$ by each term in $(3w^2 - 4w + 1)$ .
$w \times 3w^2 = 3w^3$
$w \times (-4w) = -4w^2$
$w \times 1 = w$
So, $w(3w^2 - 4w + 1) = 3w^3 - 4w^2 + w$
Multiply $-2$ by Polynomial: Multiply $-2$ by each term in $(3w^2 - 4w + 1)$ . $-2 \times 3w^2 = -6w^2$ $-2 \times (-4w) = 8w$ $-2 \times 1 = -2$ So, $-2(3w^2 - 4w + 1) = -6w^2 + 8w - 2$
Combine Results: Combine the results from Step $2$ and Step $3$ . $\newline$ $(3w^3 - 4w^2 + w) + (-6w^2 + 8w - 2)$ $\newline$ Now we combine like terms.
Combine Like Terms: Combine like terms. $\newline$ $3w^3 + (-4w^2 - 6w^2) + (w + 8w) - 2$ $\newline$ $3w^3 - 10w^2 + 9w - 2$ $\newline$ This is the simplified form of the product.

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