Question Multiply $-6x(3x^2 - 2x + 2)$ . Simplify the product.

Studdy Solution

STEP 1

Assumptions
1. We are given a polynomial expression $3x^2 - 2x + 2$ .
2. We are asked to multiply this expression by $-6x$ .
3. We will use the distributive property to multiply $-6x$ by each term in the polynomial.

STEP 2

Apply the distributive property to multiply $-6x$ with each term in the polynomial $3x^2 - 2x + 2$ .
$-6x \times (3x^2 - 2x + 2) = -6x \times 3x^2 + (-6x) \times (-2x) + (-6x) \times 2$

STEP 3

Multiply $-6x$ with the first term $3x^2$ .
$-6x \times 3x^2 = -18x^3$

STEP 4

Multiply $-6x$ with the second term $-2x$ .
$(-6x) \times (-2x) = 12x^2$

STEP 5

Multiply $-6x$ with the third term $2$ .
$(-6x) \times 2 = -12x$

STEP 6

Combine the results from steps 3, 4, and 5 to get the final expression.
$-18x^3 + 12x^2 - 12x$
The product is $-18x^3 + 12x^2 - 12x$ .

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