# Answer to Question #11060 in Algebra for Tanveer

Question #11060

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

Expert's answer

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.

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.

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