Question

Evaluate ${(-6p+\frac{1}{3}q-r)}^2$

Answer 1

Evaluate ${(-6p+\frac{1}{3}q-r)}^2={\left\{\right(-6p)+\frac{1}{3}q+(-r{)}^2\}}^2$
Using, $(a+b+c{)}^2=a^2+b^2+c^2+2ab+2bc+2ac$
$=(-6p{)}^2+{\left(\frac{1}{3}q\right)}^2+(-r{)}^2+2(-6p)\left(\frac{1}{3}q\right)+2\left(\frac{1}{3}q\right)(-r)+2(-r\left)\right(-6p)$
$=36p^2+\frac{1}{9}{q}^2+r^2-4pq-\frac{2}{3}qr+12rp$