# How do you factor completely 96x^2 - 6y^2 ?

May 18, 2018

$6 \left(4 x + y\right) \left(4 x - y\right)$

#### Explanation:

Expression $= 96 {x}^{2} - 6 {y}^{2}$

Notice that $6$ is a factor of both terms.

So, Expression $= 6 \left(16 {x}^{2} - {y}^{2}\right)$

Then notice that $\left(16 {x}^{2} - {y}^{2}\right)$ is the difference of the two squares: ${\left(4 x\right)}^{2} \mathmr{and} {y}^{2}$

Using the common identity: ${a}^{2} - {b}^{2} = \left(a + b\right) \left(a - b\right)$

Expression $= 6 \left(4 x + y\right) \left(4 x - y\right)$