Question

Simplify
(p + q + r )^2 +( p-q-r)^2​

Answer 1

$= ( {p}^{2} + {q}^{2} + {r}^{2} + 2pq + 2qr + 2pr) + {p}^{2} + {q}^{2} + {r}^{2} - 2pq + 2qr - 2pr$

$= 2( {p}^{2} + {q}^{2} + {r}^{2} ) + 4qr$

$= ( {( \sqrt{2}q) + ( \sqrt{2}r) )}^{2} + 2 {p}^{2}$