Answer
$\displaystyle \frac{1}{25}(5x-1)^{2}$
Work Step by Step
$\displaystyle \frac{25}{25}x^{2}-\frac{10}{25}x+\frac{1}{25}$
...and factor out the gcf, $\displaystyle \frac{1}{25}...$
$...=\displaystyle \frac{1}{25}(25x^{2}-10x+1)$
... breaking $-10x$ into $-5x-5x$, we can factor in groups:
$... =\displaystyle \frac{1}{25}[(25x^{2}-5x)+(-5x+1)]$
$... =\displaystyle \frac{1}{25}[5x(5x-1)-1(5x-1)]$
= $\displaystyle \frac{1}{25}(5x-1)(5x-1)$
= $\displaystyle \frac{1}{25}(5x-1)^{2}$
