Question

how can i factor this?
x^(2n)-2x^(n)+1

Answer 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