## Expanding (5x + 3)(5x - 3)

This expression is a classic example of the **difference of squares** pattern. Here's how to expand it:

### Understanding the Difference of Squares

The difference of squares pattern states:

**(a + b)(a - b) = a² - b²**

This pattern arises because when you multiply the terms, the middle terms cancel each other out:

**a * a = a²****a * -b = -ab****b * a = ab****b * -b = -b²**

The -ab and ab terms cancel, leaving only a² - b².

### Applying the Pattern

In our expression (5x + 3)(5x - 3):

**a = 5x****b = 3**

Applying the difference of squares pattern, we get:

**(5x + 3)(5x - 3) = (5x)² - (3)²**

### Simplifying the Expression

Now, we simplify by squaring the terms:

**(5x)² - (3)² = 25x² - 9**

### Conclusion

Therefore, the expanded form of (5x + 3)(5x - 3) is **25x² - 9**. This demonstrates how recognizing patterns in algebra can simplify complex expressions.