Question

determine the product of three linear factors. verify graphically that the expressions are equivalent.
sample problem
$3x(x + 3)(x - 2)$
$= 3x(x^2 - 2x + 3x - 6)$
$= 3x(x^2 + x - 6)$
$= 3x^3 + 3x^2 - 18x$
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.
$(10 - 3x)(7 + x)(8 + 6x)$
$=\square$

Explanation:

Step1: Multiply first two binomials

$$(10-3x)(7+x) = 10(7) + 10(x) - 3x(7) - 3x(x)$$
$$=70 + 10x -21x -3x^2$$
$$=70 -11x -3x^2$$

Step2: Multiply by third binomial

$$(70 -11x -3x^2)(8+6x) = 70(8) + 70(6x) -11x(8) -11x(6x) -3x^2(8) -3x^2(6x)$$
$$=560 + 420x -88x -66x^2 -24x^2 -18x^3$$

Step3: Combine like terms

$$= -18x^3 + (-66x^2-24x^2) + (420x-88x) + 560$$
$$= -18x^3 -90x^2 + 332x + 560$$

Answer:

$-18x^3 -90x^2 + 332x + 560$

Graphical verification note: To confirm equivalence, graph the original factored expression $(10-3x)(7+x)(8+6x)$ and the expanded polynomial $-18x^3 -90x^2 + 332x + 560$. The two graphs will be identical, proving the expressions are equivalent.