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

Apr 16, 2018

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

Explanation:

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

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

The sum of cubes is factored as:

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

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

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