Answer
$-a^2-2a-4$
Work Step by Step
Factoring the expressions and then cancelling the common factors between the numerator and the denominator, the given expression, $
\dfrac{a^3-8}{2-a}
$ simplifies to
\begin{array}{l}\require{cancel}
\dfrac{(a-2)(a^2+2a+4)}{-(a-2)}
\\\\=
\dfrac{(\cancel{a-2})(a^2+2a+4)}{-(\cancel{a-2})}
\\\\=
-(a^2+2a+4)
\\\\=
-a^2-2a-4
.\end{array}
