Question: User: $x^2$- $9y^2$
1. **State the problem:**
Factor the expression $$x^2 - 9y^2$$.
2. **Formula used:**
This is a difference of squares, which follows the rule:
$$a^2 - b^2 = (a - b)(a + b)$$
3. **Identify terms:**
Here, $$a = x$$ and $$b = 3y$$ because $$9y^2 = (3y)^2$$.
4. **Apply the formula:**
$$x^2 - 9y^2 = (x - 3y)(x + 3y)$$
5. **Explanation:**
The difference of squares formula allows us to factor expressions where two perfect squares are subtracted. We write the expression as the product of the sum and difference of the square roots of each term.
**Final answer:**
$$(x - 3y)(x + 3y)$$