1. **State the problem:** Simplify the expression $x^2 - 9$. 2. **Recognize the formula:** This is a difference of squares, which follows the rule: $$a^2 - b^2 = (a - b)(a + b)$$ where $a = x$ and $b = 3$ because $9 = 3^2$. 3. **Apply the formula:** $$x^2 - 9 = x^2 - 3^2 = (x - 3)(x + 3)$$ 4. **Explain:** The difference of squares factors into the product of the sum and difference of the two terms. 5. **Final answer:** $$\boxed{(x - 3)(x + 3)}$$