Question

How do you factor #x^3+1?

Answer 1

`x^3+1 = x^3 + 1^3`

The sum of cubes identity tells us that :

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

Hence `x^3 + 1^3 = (x + 1)(x^2 - (x*1) + 1^2)`

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