## Simplifying the Expression (a + b)(a - b)

The expression **(a + b)(a - b)** is a common algebraic expression that simplifies to a much simpler form. This simplification is based on the **difference of squares** pattern.

### Understanding the Difference of Squares

The difference of squares pattern states that:
**(x + y)(x - y) = x² - y²**

This pattern can be understood by expanding the expression:

**(x + y)(x - y) = x(x - y) + y(x - y)****= x² - xy + xy - y²****= x² - y²**

### Applying the Pattern to (a + b)(a - b)

Applying the difference of squares pattern to our expression **(a + b)(a - b)**, we can see that:

**a**corresponds to**x****b**corresponds to**y**

Therefore, we can simplify the expression as:

**(a + b)(a - b) = a² - b²**

### Example:

Let's say **a = 3** and **b = 2**. We can use the simplified form to calculate the value of the expression:

**(a + b)(a - b) = a² - b²**
**(3 + 2)(3 - 2) = 3² - 2²**
**(5)(1) = 9 - 4**
**5 = 5**

As you can see, the simplified form makes the calculation much easier.

### Conclusion

Simplifying expressions like **(a + b)(a - b)** using the difference of squares pattern is a valuable skill in algebra. It allows us to manipulate expressions more easily and solve equations more efficiently.