To simplify the expression \((X - y)^2 - (x + y)^2((X - y)^2 - (x + y)^2)\), let's first break it down step by step.

1. Start with the original expression:
\[
(X - y)^2 - (x + y)^2((X - y)^2 - (x + y)^2)
\]

2. Let's denote:
\[
A = (X - y)^2, \quad B = (x + y)^2
\]

The expression becomes:
\[
A - B(A - B)
\]

3. Now replace \(A - B\) with \((X - y)^2 - (x + y)^2\):
\[
A - B \cdot (A - B) = A - B(A - B) = A - (BA - B^2)
\]

4. Distributing the \(B\):
\[
A - BA + B^2
\]

Now, substituting \(A\) and \(B\) back in terms of \(X\) and \(y\):
\[
(X - y)^2 - (x+y)^2(X - y)^2 + (x+y)^4
\]

This expression is simplified, but it could potentially be expressed as a polynomial depending on the context. Each individual term can be expanded if necessary.

Overall, the expression simplifies to:
\[
(X - y)^2 - (x+y)^2(X - y)^2 + (x+y)^4
\]

You can further simplify or expand this expression based on your requirements!