x^6-64
How do I factor this problem?
The answer I'm supposed to get, I can't figure out how to get there.
you will have to know how to factor the sum and difference of cubes
i.e.
A^3 + B^3 = (A+B)(A^2 - AB + B^2) and
A^3 - B^3 = (A-B)(A^2 + AB + B^2)
so first of all we do a difference of squares
x^6-64
= (x^3+8)(x^3-8)
= (x+2)(x^2 - 2x + 4)(x-2)(x^2 + 2x + 4)