Question

(2p + q)² - (p - 2q)² =

Answer 1

(2p+q)(2p+q)=4 p la 2+4pq+q la 2
(p-2q)(p-2q)=p la 2-4pq+4 q la 2

avem:4p la 2+4pq+q la 2-p la 2+4pq-4 q la 2=3pla2+8pq-3qla2

Answer 2

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

(4p^2+2pq+2pq+q^2) - (p^2-2pq-2pq+4q^2) = 

(4p^2+4qp^2+q^2) - (p^2-4pq^2+4q^2) = 3p^2+5q^2