Question

What should be added to $x^2+\frac{1}{25}{x}^2{y}^2$ make it a perfect square

Answer 1

$x^2+\frac{1}{25}{x}^2{y}^2$

$=(x{)}^2+{\left(\frac{xy}{5}\right)}^2+2(x)\left(\frac{xy}{5}\right)$

$={(x+\frac{xy}{5})}^2$

So after adding $\frac{2x^{2}y}{5}$

We get perfect square.