Find the product. Simplify your answer. (3x - 2)(x^2 - 3x + 2) ______

Distribute Terms: Distribute each term in the first polynomial to each term in the second polynomial. 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. 3x * x^2 = 3x^3 3x * (-3x) = -9x^2 3x * 2 = 6x So we have 3x^3 - 9x^2 + 6x.Multiply -2: Multiply -2 by each term in the second polynomial. -2 * x^2 = -2x^2 -2 * (-3x) = 6x -2 * 2 = -4 So we have -2x^2 + 6x - 4.Combine Like Terms: Combine like terms from the results of Step 2 and Step 3. We add the corresponding terms from the two products: (3x^3 - 9x^2 + 6x) + (-2x^2 + 6x - 4) 3x^3 + (-9x^2 - 2x^2) + (6x + 6x) - 4 3x^3 - 11x^2 + 12x - 4

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Q. Find the product. Simplify your answer.

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(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: $\newline$ $(3x^3 - 9x^2 + 6x) + (-2x^2 + 6x - 4)$ $\newline$ $3x^3 + (-9x^2 - 2x^2) + (6x + 6x) - 4$ $\newline$ $3x^3 - 11x^2 + 12x - 4$