# How do you use the difference of two squares formula to factor 9/x^6 - 64y^2?

Jun 9, 2018

$\left(\frac{3}{x} ^ 3 - 8 y\right) \left(\frac{3}{x} ^ 6 + 8 y\right)$

#### Explanation:

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

we get

$\left(\frac{3}{x} ^ 3 - 8 y\right) \left(\frac{3}{x} ^ 4 + 8 y\right)$

Jun 9, 2018

$\left(\frac{3}{x} ^ 3 - 8 y\right) \left(\frac{3}{x} ^ 3 + 8 y\right)$

#### Explanation:

•color(white)(x)a^2-b^2=(a-b)(a+b)larrcolor(blue)"difference of squares"

$\frac{9}{x} ^ 6 = {\left(\frac{3}{x} ^ 3\right)}^{2} \Rightarrow a = \frac{3}{x} ^ 3$

$64 {y}^{2} = {\left(8 y\right)}^{2} \Rightarrow b = 8 y$

$\frac{9}{x} ^ 6 - 64 {y}^{2} = \left(\frac{3}{x} ^ 3 - 8 y\right) \left(\frac{3}{x} ^ 3 + 8 y\right)$