parmenides51 wrote: Show that if $a \ge b \ge c \ge 0$ then $$a^2b(a - b) + b^2c(b - c) + c^2a(c - a) \ge 0.$$ Let $ a$, $ b$ and $ c$ be the lengths of the sides of a triangle. Prove that \[ a^{2}b(a - b) + b^{2}c(b - c) + c^{2}a(c - a)\ge 0.\]https://artofproblemsolving.com/community/c6h325931p1747448