# How do you factor 8x^3 - y^6?

$8 {x}^{3} - {y}^{6} = {\left(2 x\right)}^{3} - {\left({y}^{2}\right)}^{3}$
We can use the Identity color(blue)(a^3 - b^3 = (a - b)(a^2 +ab+b^2)
We get $\left(2 x - {y}^{2}\right) \left\{{\left(2 x\right)}^{2} + \left(2 x\right) \left({y}^{2}\right) + {\left({y}^{2}\right)}^{2}\right\}$
 = color(green)((2x - y^2){4x^2 +2xy^2 +y^4}
As none of the factors above can be factorised further, it is the factorised form of $8 {x}^{3} - {y}^{6}$