How do you factor 64x^3+1?

Apr 22, 2015

$64 {x}^{3} + 1$

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

We know that color(blue)(a^3 + b^3 = (a+b)(a^2 - ab + b^2)

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

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

As any of the factors cannot be factorised further, this becomes the final factorised form of $64 {x}^{3} + 1$