4 variable inequality

[Guest]

Prove that [tex]\Big[(a+c)(b+d)\Big]^{2}\ge 4(ab+cd)(ad+bc),\forall a,b,c,d>0[/tex].

[Guest]

((a+c)(b+d))^2 =
((ab+cd)+(ad+bc))^2 =
(ab+cd)^2+(ad+bc)^2+2(ab+cd)(ad+bc) >= (AM/GM)
2(ab+cd)(ad+bc)+2(ab+cd)(ad+bc) =
4(ab+cd)(ad+bc)

[MM]

Nice! (I posted the problem)