Factor the following:
256 x^8-1
256 x^8-1 = (16 x^4)^2-1^2:
(16 x^4)^2-1^2
Factor the difference of two squares. (16 x^4)^2-1^2 = (16 x^4-1) (16 x^4+1):
(16 x^4-1) (16 x^4+1)
16 x^4-1 = (4 x^2)^2-1^2:
(4 x^2)^2-1^2 (16 x^4+1)
Factor the difference of two squares. (4 x^2)^2-1^2 = (4 x^2-1) (4 x^2+1):
(4 x^2-1) (4 x^2+1) (16 x^4+1)
4 x^2-1 = (2 x)^2-1^2:
(2 x)^2-1^2 (4 x^2+1) (16 x^4+1)
Factor the difference of two squares. (2 x)^2-1^2 = (2 x-1) (2 x+1):
Answer: | (2 x-1) (2 x+1) (4 x^2+1) (16 x^4+1)
