# How do you factor 36x^2-60x+25?

Aug 7, 2016

$= \left(6 x - 5\right) \left(6 x - 5\right)$

#### Explanation:

$36 {x}^{2} - 60 x + 25$
$= {\left(6 x\right)}^{2} - 2 \left(6 x\right) \left(5\right) + {5}^{2}$
$= {\left(6 x - 5\right)}^{2}$
$= \left(6 x - 5\right) \left(6 x - 5\right)$

Aug 7, 2016

${\left(6 x - 5\right)}^{2}$

#### Explanation:

since your ${x}^{2}$ has a number in front of it, you will need to multiply that by 25 first. this gives you 900 so you now must find two numbers that add to $- 60$ and multiply to $900$. as luck would have it, $- 30$ jumps out as the answer. break down the equation accordingly and factor from there.

$36 {x}^{2} - 60 x + 25$

$36 {x}^{2} - 30 x - 30 x + 25$

factor the frist two variables and then the second two

$36 {x}^{2} - 30 x - 30 x + 25$

$6 x \left(6 x - 5\right) - 5 \left(6 x - 5\right)$

format with the numbers outside the brackets as one group and the leave the others as is.

$\left(6 x - 5\right) \left(6 x - 5\right)$

this is a perfect square, ergo

${\left(6 x - 5\right)}^{2}$