Question

multiply the polynomial by the monomial using the distributive property and/or the product rule of exponents.

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

Explanation:

Identify the given expression

We are given a monomial and a binomial to multiply:

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

The monomial is \( -3x^2 \) and the polynomial is \( -2x + 2 \).

Apply the distributive property

Using the Distributive Property with Polynomials concept, we distribute the monomial to each term inside the parentheses:

$$ (-3x^2) \cdot (-2x) + (-3x^2) \cdot (2) $$

Multiply the first terms

Multiply the coefficients and apply the product rule of exponents to the variables:

$$ (-3 \cdot -2) \cdot (x^2 \cdot x^1) = 6x^{2+1} = 6x^3 $$

Multiply the second terms

Multiply the monomial by the constant term:

$$ (-3 \cdot 2) \cdot x^2 = -6x^2 $$

Combine the simplified terms

Combine the results of the multiplication steps to write the final simplified polynomial:

$$ 6x^3 - 6x^2 $$

Answer:

\(6x^3 - 6x^2\)