1. **State the problem:** Simplify the expression $ (x+y)(x-y) $. 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 $b = y$, so: $$ (x+y)(x-y) = x^2 - y^2 $$ 4. **Explanation:** When multiplying conjugates, the middle terms cancel out because one is positive and the other is negative, leaving the difference of squares. 5. **Final answer:** $$ x^2 - y^2 $$