Nice Inequality: (a + b) (a + c) (b + c) (a + d) (b + d) (c

[LanNguyen]

Can anyone help to prove this inequality that came out from a larger problem I'm working on?
I know for a fact that it's true but haven't been able to prove

Use of advanced techniques is welcome if required..

(a + b) (a + c) (b + c) (a + d) (b + d) (c + d) >= 4 a b c d (a + b + c + d)^2

for all positive a, b, c, d

Thanks

 

[mmm4444bot]

... I know for a fact that it's true ...

Hi LanNguyen:

How do you know that it is a fact?

~ Mark :|