# How do you factor # x^3 - 1#?

##### 2 Answers

Expanding upon prior answer:

#### Explanation:

I want to expand upon an idea expressed in the prior answer

The idea of:

or not in sigma notation:

We can prove this via induction:

Basis case :

Hence basis case holds

Induction:

Assume

Hence this is also what we yield when plugging directly into formula:

Hence holds for all

I thought this was a nice idea to consider!

#### Explanation:

#x^3-1" is a "color(blue)"difference of cubes"#

#â€¢color(white)(x)a^3-b^3=(a-b)(a^2+ab+b^2)#

#"here "a=x" and "b=1#

#rArrx^3-1=(x-1)(x^2+x+1)#