factorizing this:
$\displaystyle
x^4-64x
$
$\displaystyle
= (x^2+8)(x+4)(x-4)
$
correct?
I don't think so. Pull out an x immediately. $\displaystyle x(x^3-64)$. Now write 64 as a cube. $\displaystyle x(x^3-4^3)$. Now you can plug this into a difference of cubes formula.
When you expand the answer you have back out, it doesn't give the original expression.