Task 680
Task 680: development task in emrekuruu/math-openenv, an RL environment on the Hugging Face Hub. The expression \ a^3 (b^2 - c^2) + b^3 (c^2 - a^2) + c^3 (a^2 - b^2)\ can be factored into the form $(a - b)(b - c)(c - a) p(a,b,c),$ for some polynomial $p(a,b,c).$ Find $p(a,b,c).$
The task
The expression \[a^3 (b^2 - c^2) + b^3 (c^2 - a^2) + c^3 (a^2 - b^2)\]can be factored into the form $(a - b)(b - c)(c - a) p(a,b,c),$ for some polynomial $p(a,b,c).$ Find $p(a,b,c).$