# How do you factor the following difference of two cubes 64x^3-1?

Mar 26, 2018

color(blue)((4x-1)(16x^2+4x+1)

#### Explanation:

The difference of two cubes an be expressed as:

$\left({a}^{3} - {b}^{3}\right) = \left(a - b\right) \left({a}^{2} + a b + {b}^{2}\right)$

Notice we can write:

$64 {x}^{3} = {4}^{3} {x}^{3} = {\left(4 x\right)}^{3}$

$\therefore$

$\left({\left(4 x\right)}^{3} - {1}^{3}\right) = \left(4 x - 1\right) \left({\left(4 x\right)}^{2} + \left(4 x\right) \left(1\right) + {\left(1\right)}^{2}\right)$

((4x)^3-1^3)=color(blue)((4x-1)(16x^2+4x+1)