1. **State the problem:** We are given the equation $x^3 + y^3 = 20$ and want to understand or analyze it. 2. **Formula and rules:** This is an equation involving cubes of two variables. The sum of cubes formula is $a^3 + b^3 = (a+b)(a^2 - ab + b^2)$, but here it equals a constant 20. 3. **Intermediate work:** We can rewrite the equation as $$x^3 + y^3 = 20.$$ There is no direct simplification without additional conditions. 4. **Explanation:** This equation represents a curve in the $xy$-plane. For any $x$, $y$ satisfies $y^3 = 20 - x^3$, so $$y = \sqrt[3]{20 - x^3}.$$ This function is defined for all real $x$ where $20 - x^3$ is real. 5. **Summary:** The equation describes the set of points $(x,y)$ such that the sum of their cubes is 20. The function $y = \sqrt[3]{20 - x^3}$ can be graphed to visualize this curve.