Question

(x^2n - y^n)(x^2n -Y^n)

Answer 1

That looks like the same thing as (x^2n - y^n)^2

If you multiply it out, you get
x^4n - 2 x^2n*y^n + y^2n

Answer 2

You should stick with upper or lower case letters (y and Y in your case) and not mix them up. It can lead to confusion. I assumed you meant them both to be the same.