SymmetricReduction[(a^2 c + b c^2 + a b^2) (a^2 b + b^2 c + a c^2), {a, b, c}]

Uh oh! Wolfram|Alpha doesn't run without JavaScript.

Please enable JavaScript. If you don't know how, you can find instructionshere.Once you've done that, refresh this page to start using Wolfram|Alpha.