SOLUTION: How do I factor completely x^8-1?

Question 152956: How do I factor completely x^8-1?
Found 2 solutions by scott8148, jim_thompson5910:
Answer by scott8148(6628) (Show Source): You can put this solution on YOUR website!
this factors multiple times using the difference of squares

x^8-1=(x^4-1)(x^4+1)

x^4-1=(x^2-1)(x^2+1)

x^2-1=(x-1)(x+1)

x^8-1=(x^4+1)(x^2+1)(x+1)(x-1)
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

Start with the given expression

Rewrite as . Rewrite as

Factor using the difference of squares formula. Remember, the difference of squares formula is

Rewrite as . Rewrite as .

Factor using the difference of squares formula

Rewrite as .

Factor using the difference of squares formula

So the expression factors to

In other words,
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