Question

p(p+q)2-(p-q)(p2+pq+q2)

Answer 1

p(p+q)2-(p-q)(p2+pq+q2)

= p(p+q)2-(p-q) [ (p2+2pq+q2) - pq ]

= p(p+q)2-(p-q) [ (p+q)2 - pq ]

= p(p+q)2- (p-q) ( p+q)2 + pq (p-q)

= ( p+q)2 ( p -p+q ) + pq (p-q)

= q ( p+q)2 + pq (p-q)

= q ( p² +q² +2pq + p² -q² )

= q ( 2p² +2pq)

= 2pq ( p +q )