Question: Factor the following if possible.
49n^2 - 81
Select the correct response:
(7n - 9)^2
1. **State the problem:** Factor the expression $$49n^2 - 81$$.
2. **Recognize the formula:** This is a difference of squares since $$49n^2 = (7n)^2$$ and $$81 = 9^2$$.
3. **Difference of squares formula:** $$a^2 - b^2 = (a - b)(a + b)$$.
4. **Apply the formula:**
$$49n^2 - 81 = (7n)^2 - 9^2 = (7n - 9)(7n + 9)$$.
5. **Check the given option:** The option $$(7n - 9)^2$$ is a perfect square, which expands to $$49n^2 - 2 \cdot 7n \cdot 9 + 81 = 49n^2 - 126n + 81$$, not matching the original expression.
6. **Conclusion:** The correct factorization is $$(7n - 9)(7n + 9)$$, so the given option is incorrect.