1. **State the problem:** Given that $$(x+y)^2=600$$, $$x^2=60$$, and $$y^2=40$$, find the value of $$xy$$. 2. **Recall the formula:** The expansion of $$(x+y)^2$$ is $$x^2 + 2xy + y^2$$. 3. **Substitute the known values:** $$600 = 60 + 2xy + 40$$ 4. **Simplify the equation:** $$600 = 100 + 2xy$$ 5. **Isolate $$2xy$$:** $$600 - 100 = 2xy$$ $$500 = 2xy$$ 6. **Solve for $$xy$$:** $$xy = \frac{500}{2}$$ $$xy = 250$$ **Final answer:** $$xy = 250$$