1. **State the problem:** Factor the expression $x^2 - 81$. 2. **Recall the formula:** This is a difference of squares, which follows the rule: $$a^2 - b^2 = (a - b)(a + b)$$ 3. **Identify terms:** Here, $a = x$ and $b = 9$ because $81 = 9^2$. 4. **Apply the formula:** $$x^2 - 81 = (x - 9)(x + 9)$$ 5. **Explanation:** The difference of squares factors into the product of the sum and difference of the square roots of the terms. **Final answer:** $$x^2 - 81 = (x - 9)(x + 9)$$