To understand Rearrangement Inequality just look at x>y>z as two separate sequences. I mean

x>y>z and

x>y>z.

 

RI tells us x²+y²+z²> xy+yz+zx.

 

 or x³+y³+z³> x²y+y²z+z²x (by also looking at x²>y²>z²).

 

You can read it about this fascinating inequality on many sites on the Internet.