Question

4(2 - 3w)(w² - 2w + 10)

Explanation:

Step1: Multiply \((2 - 3w)\) and \((w^2 - 2w + 10)\)

Using the distributive property (FOIL for polynomials):
\[

$$\begin{align*} (2 - 3w)(w^2 - 2w + 10)&=2(w^2 - 2w + 10)-3w(w^2 - 2w + 10)\\ &=2w^2 - 4w + 20 - 3w^3 + 6w^2 - 30w \end{align*}$$

\]
Combine like terms:
\[
-3w^3+(2w^2 + 6w^2)+(-4w - 30w)+20=-3w^3 + 8w^2 - 34w + 20
\]

Step2: Multiply by 4

\[
4(-3w^3 + 8w^2 - 34w + 20)=-12w^3 + 32w^2 - 136w + 80
\]

Answer:

\(-12w^3 + 32w^2 - 136w + 80\)