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

1 Answer
Sep 11, 2016

Answer:

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

Explanation:

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)#