1. **State the problem:** Simplify the expression $$(x-3)(x+3)$$. 2. **Formula used:** This is a product of conjugates, which follows the identity $$ (a-b)(a+b) = a^2 - b^2 $$. 3. **Apply the formula:** Here, $a = x$ and $b = 3$, so $$ (x-3)(x+3) = x^2 - 3^2 $$. 4. **Simplify:** $$ x^2 - 9 $$. 5. **Explanation:** Multiplying conjugates results in the difference of squares, which eliminates the middle term and simplifies the expression. **Final answer:** $$x^2 - 9$$.