Answer
$a^2(a^{n}-3)(a^n+2)$.
Work Step by Step
The given expression is
$=a^{2n+2}-a^{n+2}-6a^2$
$=a^{2n}a^2-a^{n}a^2-6a^2$
Factor out $a^2$.
$=a^2(a^{2n}-a^{n}-6)$
Rewrite the term $-a^{n}$ as $-3a^{n}+2a^{n}$.
$=a^2(a^{2n}-3a^{n}+2a^{n}-6)$
Group terms.
$=a^2[(a^{2n}-3a^{n})+(2a^{n}-6)]$
Factor from each group.
$=a^2[a^n(a^{n}-3)+2(a^{n}-3)]$
Factor out $(a^n-3)$
$=a^2(a^{n}-3)(a^n+2)$.
