Question

How do you factor `64x^3+1`?

Answer 1

`64x^3+1`

`= (4x)^3 + 1^3`

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

`= (4x + 1)((4x)^2 -(4x)(1) + 1^2)`

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

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