Answer
$b^2(b^n-2)(b^{n}+5)$.
Work Step by Step
The given expression is
$=b^{2n+2}+3b^{n+2}-10b^2$
$=b^{2n}b^2+3b^{n}b^2-10b^2$
Factor out $b^2$.
$=b^2(b^{2n}+3b^{n}-10)$
Rewrite the term $3b^{n}$ as $5b^{n}-2b^{n}$.
$=b^2(b^{2n}+5b^{n}-2b^{n}-10)$
Group terms.
$=b^2[(b^{2n}+5b^{n})+(-2b^{n}-10)]$
Factor from each group.
$=b^2[b^n(b^{n}+5)-2(b^{n}+5)]$
Factor out $(b^{n}+5)$
$=b^2(b^{n}+5)(b^n-2)$.
Rearrange.
$=b^2(b^n-2)(b^{n}+5)$.
