Answer to Question #11060 in Algebra for Tanveer

Question

prove that, p(q^2+r^2)+q(p^2+r^2)+r(p^2+q^2)=0.

Answer 1

If we denote

g1=p+q+r
g2=pq+qr+pr
g3=pqr

then
p(q^2+r^2)+q(p^2+r^2)+r(p^2+q^2)=g1*g2-3*g3
If
g1=g3=0 then given expression is zero too.