(x^2n - y^n)(x^2n -Y^n)
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
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.
To simplify the expression (x^2n - y^n)(x^2n - Y^n), you can use the difference of squares formula. The formula states that a^2 - b^2 can be factored into (a + b)(a - b).
In this case, let's consider x^2n as "a" and y^n as "b". So the expression can be rewritten as:
[(x^2n)^2 - (y^n)^2]
Applying the difference of squares formula, we get:
[(x^2n + y^n)(x^2n - y^n)]
Now let's move on to the second part, (x^2n - Y^n). Notice that we have a discrepancy between the variable "y" and "Y". Assuming they represent the same value, we can proceed with the simplification.
Similarly, applying the difference of squares formula to this part, we get:
[(x^2n + Y^n)(x^2n - Y^n)]
Therefore, the overall simplified expression is:
[(x^2n + y^n)(x^2n - y^n)][(x^2n + Y^n)(x^2n - Y^n)]