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

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Multiply polynomials

Full solution

Q. Find the product. Simplify your answer.

\newline

(3x - 2)(x^2 - 3x + 2)

Distribute Terms: Distribute each term in the first polynomial to each term in the second polynomial. $\newline$ We will use the distributive property $a(b + c) = ab + ac$ to multiply each term in the first polynomial $3x - 2$ by each term in the second polynomial $x^2 - 3x + 2$ .
Multiply $3x$ : Multiply $3x$ by each term in the second polynomial. $\newline$ $3x \times x^2 = 3x^3$ $\newline$ $3x \times (-3x) = -9x^2$ $\newline$ $3x \times 2 = 6x$ $\newline$ So we have $3x^3 - 9x^2 + 6x$ .
Multiply $-2$ : Multiply $-2$ by each term in the second polynomial. $\newline$ $-2 \times x^2 = -2x^2$ $\newline$ $-2 \times (-3x) = 6x$ $\newline$ $-2 \times 2 = -4$ $\newline$ So we have $-2x^2 + 6x - 4$ .
Combine Like Terms: Combine like terms from the results of Step $2$ and Step $3$ . $\newline$ We add the corresponding terms from the two products: $\newline$ $(3x^3 - 9x^2 + 6x) + (-2x^2 + 6x - 4)$ $\newline$ $3x^3 + (-9x^2 - 2x^2) + (6x + 6x) - 4$ $\newline$ $3x^3 - 11x^2 + 12x - 4$

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