Question

determine the product of linear and quadratic factors. verify
sample problem
$x(x^2 + 3x - 4)$
$x(x^2 + 3x - 4)=x^3 + 3x^2 - 4x$
the graph of the original expression and the graph of the final expression are the same. so the expressions are equivalent.
type the answer in the space provided. use numbers instead of words.
$(x^2 + 1)(8 - x)$
$=\boxed{}$

Explanation:

Step1: Distribute $x^2$ to $(8-x)$

$$\begin{aligned} x^2(8-x) = 8x^2 - x^3 \end{aligned}$$

Step2: Distribute $1$ to $(8-x)$

$$\begin{aligned} 1(8-x) = 8 - x \end{aligned}$$

Step3: Combine the two results

$$\begin{aligned} (8x^2 - x^3) + (8 - x) = -x^3 + 8x^2 - x + 8 \end{aligned}$$

Answer:

$\boldsymbol{-x^3 + 8x^2 - x + 8}$