How do you factor #64x^3-1#?
The difference of cubes formula states that:
(try multiplying the right side to verify this)
Applying this, we have:
If we wished to factor further, we could apply the quadratic formula to find the roots of
As we have the square root of a negative number, we have no real solutions, and so are done if we are using only real numbers. If we allow for complex numbers, then using
and thus, remembering to multiply by