# How do you factor completely #7x^3-56 #?

##### 1 Answer

Sep 25, 2016

#### Explanation:

The difference of cubes identity can be written:

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

We use this with

First note that both terms are divisible by

#7x^3-56 = 7(x^3-8)#

#color(white)(7x^3-56) = 7(x^3-2^3)#

#color(white)(7x^3-56) = 7(x-2)(x^2+2x+4)#

This is as far as we can go with Real coefficients. If we allow Complex coefficients, then this factors further as:

#color(white)(7x^3-56) = 7(x-2)(x-2omega)(x-2omega^2)#

where