## Understanding the Expansion of (a + 3)(a - 3)

The expression (a + 3)(a - 3) represents the product of two binomials. To understand its expansion, we can utilize the **FOIL method**, which stands for **First, Outer, Inner, Last**.

### Expanding Using FOIL Method

**First:**Multiply the first terms of each binomial: a * a =**a²****Outer:**Multiply the outer terms of the binomials: a * -3 =**-3a****Inner:**Multiply the inner terms of the binomials: 3 * a =**3a****Last:**Multiply the last terms of each binomial: 3 * -3 =**-9**

Now, we combine all the terms: a² - 3a + 3a - 9

Finally, we simplify by combining the like terms: **a² - 9**

### The Difference of Squares Pattern

The expansion of (a + 3)(a - 3) results in **a² - 9**. This is a classic example of the **difference of squares pattern**.

**The Difference of Squares Pattern:**
(x + y)(x - y) = x² - y²

In our case, x = a and y = 3.

### Significance of the Difference of Squares

The difference of squares pattern is a valuable tool for factoring and simplifying algebraic expressions. It helps us recognize and manipulate expressions that follow this specific pattern.

**Example:**

If we encounter an expression like a² - 16, we can recognize it as the difference of squares (a² - 4²). Therefore, we can factor it as (a + 4)(a - 4).

### Conclusion

The expansion of (a + 3)(a - 3) demonstrates the application of the FOIL method and the difference of squares pattern. By understanding these concepts, we can effectively simplify and manipulate algebraic expressions, making calculations and problem-solving more efficient.