How can i factor this?

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

You can make it easier by replacing x^n with another variable, factoring, then putting x^n back in the end.

Using exponent and algebra rules, rewrite x^2n - 2x^n + 1 as

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

Then, let x^n = m.

m^2 - 2m + 1

Now factor that: (m - 1) ^2

And now put x^n back: (x^n - 1) ^2