Question

Add : $p(p-q),q(q-r)andr(r-p)$

Answer 1

To add : $p(p-q),q(q-r)andr(r-p)$

$\begin{array}{rcl}& & \text{Sum of}\text{p(p – q), q(q – r) and r(r – p)}\\ & & \text{= p( p – q) + q(q – r) + r( r – p)}\\ & & {\text{= (p}}^{\text{2}}{\text{– pq) + (q}}^{\text{2}}{\text{– qr) + (r}}^{\text{2}}\text{– pr)}\\ & & {\text{= p}}^{\text{2}}{\text{– pq + q}}^{\text{2}}{\text{– qr + r}}^{\text{2}}\text{– pr}\\ & & {\text{= p}}^{\text{2}}{\text{+ q}}^{\text{2}}{\text{+ r}}^{\text{2}}\text{– pq – qr – pr}\end{array}$

Hence, On adding $p(p-q),q(q-r)andr(r-p)$ we get, ${\text{p}}^2{\text{+q}}^2{\text{+r}}^2\text{-pq-qr-pr}$.