# How do you factor (x^2+8)^2-36x^2?

Nov 5, 2015

$\left({x}^{2} + 6 x + 8\right) \left({x}^{2} - 6 x + 8\right)$

#### Explanation:

As you can see, you have the difference of two squares: ${\left({x}^{2} + 8\right)}^{2}$ is obviously the square of $\left({x}^{2} + 8\right)$, and $36 {x}^{2}$ is the square of $6 x$.

A known formula states that the difference of squares is

${a}^{2} - {b}^{2} = \left(a - b\right) \left(a + b\right)$

So, we have that

${\left({x}^{2} + 8\right)}^{2} - 36 {x}^{2} = \left({x}^{2} + 8 + 6 x\right) \left({x}^{2} + 8 - 6 x\right)$