Question

How do you write `x^3-1` in factored form?

Answer 1

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

Explanation:

This is a type of factorising called the the sum or difference of two cubes:

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

The sum of cubes is factored as:

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

In this case we have: `x^3 -1` so follow the rule above.

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