posted by claire .
can someone explain to me how i should factor this problem?
How do I know if i'm supposed to use the difference of two squares, or the difference of cubes?
Start with (x^3 - 8)(x^3 + 8).
One factor of x^3 -8 is (x-2). The other is(x^3 -8)/(x-2) = x^2 + 2x + 4.
The other factors are complex numbers, such as x + 2i. I assume they are not wanted.
You are left with
(x-2)(x^2 + 2x + 4)(x^3 + 8)