How do you factor completely #x^4 - 1#?

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Answer 1 · 2016-09-11T13:18:03

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

We have: #x^(4) - 1#

We can express #x^(4)# as #(x^(2))^(2)#:

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

Now that we have a difference of two squares we can factorise in the following way:

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

We now have another difference of two squares.

Let's factorise again to get:

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