Factor completely x^9-216

We'll re-write the given expression as a difference of two
cubes:

x^9 - 216 = (x^3)^3 -
(6)^3

We'll apply the
formula:

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

We'll put a = x^3 and b =
6

We'll substitute a and b into the formula
(*):

The completely factorised expression
is:

(x^3)^3 - 216 = (x^3 - 6)(x^6 + 6x^3 +
36)