1. **State the problem:** Factor the expression $9x^2 - 16$. 2. **Formula used:** This is a difference of squares, which follows the rule: $$a^2 - b^2 = (a - b)(a + b)$$ 3. **Identify squares:** Here, $9x^2 = (3x)^2$ and $16 = 4^2$. 4. **Apply the difference of squares formula:** $$9x^2 - 16 = (3x)^2 - 4^2 = (3x - 4)(3x + 4)$$ 5. **Explanation:** The expression is factored into two binomials where the first term is the positive square root of the first square and the second term is the positive square root of the second square, with opposite signs. **Final answer:** $$(3x - 4)(3x + 4)$$