Question

simplify: (p+q+r)^2+(P-q+r)^2

Answer 1

In this we will use an identity..
(a+b+c)^2=a^2 + b^2 + c^2 +2ab+2bc+2ca
so,
(p+q+r)^2 + (p+q-r)^2
=p^2+q^2+r^2+2pq+2pr+2rq+p^2+q^2+r^2+2pq-2qr-2pr
=2(p^2+q^2+r^2+2pq)
=2((p+q)^2 + r^2)

Answer 2

Using,
(a+b+c)²=a² + b²+ c² +2(ab+bc+ca)
∴(p+q+r)² + (p+q-r)²⇒p²+q²+r²+2(pq+pr+rq)+p²+q²+r²+2(pq-qr-pr)
⇒2(p²+q²+r²+2pq)
⇒2{(p+q)² + r²}
⇒2(p+q)²+2r²