Question

How do you factor `x^3-729`?

Answer 1

`(x-9)(x^2+9x+81)`

Explanation:

You have to observe that `729=9^3`, and so `x^3-729` is a difference of cubes.

In general, you have that

`a^3-b^3 = (a-b)(a^2+ab+b^2)`,

and `(a^2+ab+b^2)` is no longer factorizable (it is also known as "false square", because it resembles `(a+b)^2`, but the mixed product is halved).

In your case, `a=x` and `b=9`, so we have

`x^3-9^3 = (x-9)(x^2+9x+81)`