Let's simplify the expression \((2a - b)^2 - 4(2a - b)^2 (a - b)^2\).

First, we will express it in a clearer form:

\[
(2a - b)^2 - 4(2a - b)^2 (a - b)^2
\]

We can factor out \((2a - b)^2\) from both terms:

\[
= (2a - b)^2 [1 - 4(a - b)^2]
\]

Now, we simplify the expression inside the brackets:

\[
1 - 4(a - b)^2
\]

This expression is a difference that represents a quadratic form. It does not simplify further without specific values for \(a\) and \(b\). Therefore, the final simplified form of the expression is:

\[
(2a - b)^2 [1 - 4(a - b)^2]
\]

If you need any further operations on this expression or if you have specific values for \(a\) and \(b\) to substitute, please let me know!