# How do you factor 5x^2-5y^2+mx^2-my^2?

Jul 10, 2015

The answer is $\left(5 + m\right) \left(x + y\right) \left(x - y\right)$.

#### Explanation:

$5 {x}^{2} - 5 {y}^{2} + m {x}^{2} - m {y}^{2}$

Group the first two and last two terms together.

$\left(5 {x}^{2} - 5 {y}^{2}\right) + \left(m {x}^{2} - m {y}^{2}\right)$

Factor out the GCF for each group.

$5 \left({x}^{2} - {y}^{2}\right) + m \left({x}^{2} - {y}^{2}\right)$

${x}^{2} - {y}^{2} = \left(x + y\right) \left(x - y\right)$

$5 \left(x + y\right) \left(x - y\right) + m \left(x + y\right) \left(x - y\right)$

Factor out the $\left(x + y\right) \left(x - y\right)$.

$\left(5 + m\right) \left(x + y\right) \left(x - y\right)$