# How do you factor 36 ( 2x-y)^2 - 25 (u-2y)^2?

Apr 22, 2016

$36 {\left(2 x - y\right)}^{2} - 25 {\left(u - 2 y\right)}^{2}$

= $\left(12 x + 5 u - 16 y\right) \left(12 x - 5 u + 4 y\right)$

#### Explanation:

As $36 {\left(2 x - y\right)}^{2} - 25 {\left(u - 2 y\right)}^{2}$ is of the form ${a}^{2} - {b}^{2}$ and ${a}^{2} - {b}^{2} = \left(a + b\right) \left(a - b\right)$

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

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

= $\left[6 \left(2 x - y\right) + 5 \left(u - 2 y\right)\right] \times \left[6 \left(2 x - y\right) - 5 \left(u - 2 y\right)\right]$

= $\left[12 x - 6 y + 5 u - 10 y\right] \times \left[12 x - 6 y - 5 u + 10 y\right]$

= $\left[12 x + 5 u - 16 y\right] \times \left[12 x - 5 u + 4 y\right]$