Answer
Constant $=\frac{1}{25}$.
Perfect square trinomial $=x^2+\frac{2}{5}x+\frac{1}{25}$.
Factor form $=(x+\frac{1}{5})^2$.
Work Step by Step
The given expression is in the form of $x^2+bx$ where $b=\frac{2}{5}$.
Add $\left (\frac{b}{2} \right )^2$ to complete the square.
Therefore we add
$=\left (\frac{b}{2} \right )^2$
$=\left (\frac{2}{2\cdot5} \right )^2$
$=\left (\frac{1}{5} \right )^2$
$=\frac{1}{25}$
Hence, the perfect square trinomial is
$=x^2+\frac{2}{5}x+\frac{1}{25}$
Perfect square in the factor form is
$=\left (x+\frac{b}{2} \right )^2$
$=(x+\frac{1}{5})^2$.
