Answer
$(2-a)(4+2a+a^2)$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To factor the given expression, $
8-a^3
,$ use the factoring of the sum/difference of $2$ cubes.
$\bf{\text{Solution Details:}}$
The expressions $
8
$ and $
a^3
$ are both perfect cubes (the cube root is exact). Hence, $
8-a^3
$ is a $\text{
difference
}$ of $2$ cubes. Using the factoring of the sum or difference of $2$ cubes which is given by $a^3+b^3=(a+b)(a^2-ab+b^2)$ or by $a^3-b^3=(a-b)(a^2+ab+b^2)$ the expression above is equivalent to
\begin{array}{l}\require{cancel}
(2)^3-(a)^3
\\\\=
(2-a)[(2)^2+2(a)+(a)^2]
\\\\=
(2-a)(4+2a+a^2)
.\end{array}
