# How do you factor x^3-8y^3?

Apr 9, 2015

We can write this expression as ${x}^{3} - {\left(2 y\right)}^{3}$

The formula for factorizing the Difference of two Cubes is:
a^3−b^3=(a−b)(a^2+ab+b^2)

In ${x}^{3} - {\left(2 y\right)}^{3}$,
$a = x$
$b = 2 y$

${x}^{3} - {\left(2 y\right)}^{3}$
$= \left(x - 2 y\right) \cdot \left({x}^{2} + \left(x \cdot 2 y\right) + {\left(2 y\right)}^{2}\right)$
= color(green)( (x-2y)*(x^2+2xy+4y^2)

As we cannot factorize any of the factors further, we can say that we have factorised ${x}^{3} - 8 {y}^{3}$ completely.