If the expression $(x^3-x^2y+xy^2+y^3)^3$ is expanded and simplified, what is the sum of all the coefficients of the resulting polynomial?
I know the answer is 8, and I think last time I did it I just listed out all the terms (yes it may seem stupid but I didn't have a lot of choice due to my lack of knowledge). Does anyone know how to do this not with my way? PS this problem is from the 2014 SDHMC problem 16, and all they gave me was an answer 8. No specific explanation so I had to ask.