# How do you factor #x^9 - x^6 - x^3 + 1#?

##### 2 Answers

#### Explanation:

#### Explanation:

Let's revise our power rules ( they will come in handy later ):

- Difference of squares rule:
#x^2-y^2=(x-y)(x+y)# - Difference of cubes rule:
#x^3-y^3=(x-y)(x^2+xy+y^2)# - Sum of cubes rule:
#x^3+y^3=(x+y)(x^2-xy+y^2)#

Factorise

Factorise

Apply difference of squares rule to

Apply sum of cubes rule to

Apply difference of cubes rule to

Simplify like polynomials,

There you go.

P.S. I did not include the sum of squares rule because that rule dwells into imaginary numbers but if you are keen to know, here it is: