## Simplifying the Expression: (7/2a - 5/2b)^2 - (5/2a - 7/2b)^2

This article will guide you through simplifying the expression **(7/2a - 5/2b)^2 - (5/2a - 7/2b)^2**. We'll use algebraic manipulation and some key identities to achieve a concise result.

### Recognizing the Pattern

The given expression looks a bit intimidating at first, but there's a pattern we can exploit. Notice that both terms are squared differences. This suggests we can utilize the "difference of squares" factorization:

**(a - b)^2 - (c - d)^2 = (a - b + c - d)(a - b - c + d)**

### Applying the Factorization

Let's apply this factorization to our problem:

**a = 7/2a****b = 5/2b****c = 5/2a****d = 7/2b**

Substituting these values into the factorization, we get:

**(7/2a - 5/2b + 5/2a - 7/2b)(7/2a - 5/2b - 5/2a + 7/2b)**

### Simplifying Further

Now we can combine like terms:

**(12/2a - 12/2b)(2/2b - 2/2a)**

Simplifying the fractions:

**(6a - 6b)(b - a)**

### Final Result

Therefore, the simplified expression is **(6a - 6b)(b - a)**. This result is much more manageable than the original expression, and it highlights the importance of recognizing patterns in algebraic expressions.