1. **State the problem:** Simplify the expression $4x^2 - 9$. 2. **Recognize the formula:** This expression is a difference of squares, which follows the formula: $$a^2 - b^2 = (a - b)(a + b)$$ where $a^2 = 4x^2$ and $b^2 = 9$. 3. **Identify $a$ and $b$:** $$a = 2x, \quad b = 3$$ 4. **Apply the difference of squares formula:** $$4x^2 - 9 = (2x - 3)(2x + 3)$$ 5. **Final answer:** The factorization of $4x^2 - 9$ is $$\boxed{(2x - 3)(2x + 3)}$$