Step 1. Distribute sum groups
x(x^2 - 3xy + 2y^2) +y(x^2 - 3xy + 2y^2)
Step 2. Distribute
x^3 - 3x^2y + 2xy^2 + y(x^2 - 3xy + 2y^2)
Step 3. Distribute
x^3 - 3x^2y + 2xy^2 + yx^2 - 3y^2x + 2y^3
Step 4. Collect like terms
x^3 + (-3x^2y + x^2y) + (2xy^2) + 2y^3
Step 5. Simplify
Answer: x^3 - 2x^2y - xy^2 + 2y^3