Answer
$5(2p-9q)(p+4q)$
Work Step by Step
$10p^{2}-5pq-180q^{2}=$
...factor out the GCF.
$=5(2p^{2}-pq-36q^{2})$
...rewrite $-pq$ as $8pq-9pq$.
$=5(2p^{2}+8pq-9pq-36q^{2})$
...factor by grouping.
$=5[2p(p+4q)-9q(p+4q)]$
...factor again.
$=5(2p-9q)(p+4q)$
