1. **Problem:** Factor the expression $$16n^2 - 9$$ completely. 2. **Formula and rules:** This is a difference of squares, which factors as $$a^2 - b^2 = (a + b)(a - b)$$. 3. **Identify squares:** Here, $$16n^2 = (4n)^2$$ and $$9 = 3^2$$. 4. **Apply the formula:** $$16n^2 - 9 = (4n)^2 - 3^2 = (4n + 3)(4n - 3)$$ 5. **Explanation:** The difference of squares rule allows us to write the expression as the product of the sum and difference of the square roots. 6. **Final answer:** $$(4n + 3)(4n - 3)$$