For $a,b,c,d \geq 0$ with $a + b = c + d = 2$, prove \[(a^2 + c^2)(a^2 + d^2)(b^2 + c^2)(b^2 + d^2) \leq 25\]
Source: Singapore Senior Math Olympiad 2012 2nd Round p5 SMO
Tags: inequalities, algebra
For $a,b,c,d \geq 0$ with $a + b = c + d = 2$, prove \[(a^2 + c^2)(a^2 + d^2)(b^2 + c^2)(b^2 + d^2) \leq 25\]