Let's simplify the expression step by step. The expression you provided is:

\[
(1 - \frac{1}{2})(1 - \frac{1}{3})(1 - \frac{1}{4})(1 - \frac{1}{5}) \cdots (1 - \frac{1}{2024})(1 - \frac{1}{2025}) \times (1 - \frac{1}{2})(1 - \frac{1}{3})(1 - \frac{1}{4})(1 - \frac{1}{5}) \cdots (1 - \frac{1}{2024})(1 - \frac{1}{2025})
\]

First, we know that each term can be simplified as follows:

\[
1 - \frac{1}{n} = \frac{n-1}{n}
\]

Thus, we can rewrite the product for each term up to \(2025\) as:

\[
(1 - \frac{1}{2}) = \frac{1}{2}, \quad (1 - \frac{1}{3}) = \frac{2}{3}, \quad (1 - \frac{1}{4}) = \frac{3}{4}, \quad (1 - \frac{1}{5}) = \frac{4}{5}
\]

Continuing this way, we find:

\[
(1 - \frac{1}{n}) = \frac{n-1}{n} \text{ for } n = 2, 3, 4, 5, \ldots, 2025
\]

Now, let's express the entire product:

\[
\prod_{n=2}^{2025} \left(1 - \frac{1}{n}\right) = \prod_{n=2}^{2025} \frac{n-1}{n} = \frac{1}{2} \times \frac{2}{3} \times \frac{3}{4} \times \frac{4}{5} \times \cdots \times \frac{2024}{2025}
\]

This product is a telescoping series:

\[
\frac{1}{2025}
\]

Thus, we have:

\[
\prod_{n=2}^{2025} \left(1 - \frac{1}{n}\right) = \frac{1}{2025}
\]

Since the original expression consists of this product multiplied by itself, we have:

\[
\left( \frac{1}{2025} \right) \times \left( \frac{1}{2025} \right) = \frac{1}{2025^2}
\]

Therefore, the final result is:

\[
\frac{1}{2025^2}
\]