# How do you factor 125u^2-50u+5?

Aug 12, 2016

Factor by breaking into pieces by first taking out the 5 to give
$5 \left(25 {x}^{2} - 10 x + 1\right)$ which factors to
= $5 \left(5 x - 1\right) \left(5 x - 1\right)$
=$5 {\left(5 x - 1\right)}^{2}$

#### Explanation:

There is a common factor of 5 in all three terms. Dividing out the common factor simplifies the expression so

$125 {x}^{2} - 50 x + 5$ = $5 \left(25 {x}^{2} - 10 x + 1\right)$

This is a perfect square trinomial.

25 can be factored into 5 x 5 and 1 can be factored into 1 x1

The trinomial factor can now be factored into two binomials

$5 \left(25 {x}^{2} - 10 x + 1\right)$

=$5 \left(5 x - 1\right) \left(5 x - 1\right)$

=$5 {\left(5 x - 1\right)}^{2}$