Resolve[ForAll[{x,y},x^4 (x - y) (x - 1) + y^4 (y - 1) (y - x) + (1 - x) (1 - y)>=0]]

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.