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:

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

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