1. **Problem:** Factor the expression $16n^2 - 9$ completely. 2. **Formula:** Recognize this as a difference of squares: $$a^2 - b^2 = (a + b)(a - b)$$ 3. **Identify terms:** Here, $16n^2 = (4n)^2$ and $9 = 3^2$. 4. **Apply formula:** $$16n^2 - 9 = (4n)^2 - 3^2 = (4n + 3)(4n - 3)$$ 5. **Explanation:** The difference of squares formula allows us to factor expressions where two perfect squares are subtracted. 6. **Final answer:** $$(4n + 3)(4n - 3)$$