Question

factor: $8 + x^3$
a $(2 + x)(4 - 2x + x^2)$
b $(2 + x)^3$
c $(2 - x)(4 + 2x + x^2)$
d $(2 + x)(4 + x^2)$

$a^2 + 2ab + b^2 = (a + b)^2$
$a^2 - 2ab + b^2 = (a - b)^2$
$a^3 + b^3 = (a + b)(a^2 - ab + b^2)$
$a^3 - b^3 = (a - b)(a^2 + ab + b^2)$

Explanation:

Step1: Identify the formula

The expression \(8 + x^3\) is a sum of cubes. The formula for factoring a sum of cubes is \(a^3 + b^3=(a + b)(a^2 - ab + b^2)\).

Step2: Determine \(a\) and \(b\)

We can rewrite \(8\) as \(2^3\), so \(a = 2\) and \(b = x\) (since \(x^3\) is \(x\) cubed).

Step3: Apply the formula

Substitute \(a = 2\) and \(b = x\) into the sum of cubes formula:
\[

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

\]

Answer:

A. \((2 + x)(4 - 2x + x^2)\)