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.

$(2x - 1)(2x + 1)(x + 4)$
$=\square$

Explanation:

Step1: Multiply first two binomials

First, expand $(2x-1)(2x+1)$ using the difference of squares formula $(a-b)(a+b)=a^2-b^2$:

$$\begin{align*} (2x-1)(2x+1)&=(2x)^2-(1)^2\\ &=4x^2-1 \end{align*}$$

Step2: Multiply result with third binomial

Multiply $(4x^2-1)$ by $(x+4)$ using the distributive property:

$$\begin{align*} (4x^2-1)(x+4)&=4x^2(x)+4x^2(4)-1(x)-1(4)\\ &=4x^3+16x^2-x-4 \end{align*}$$

Answer:

$4x^3+16x^2-x-4$