If a, b, x, y are positive, then (ab + xy) (ax + by) is
> 4abxy
Since a,b,x,y are positive , ab,xy,ax,by are also positive we know
Arithmetic mean > Geometric mean
ab+xy2 > √(ab)(xy)
⇒ ab + xy >2 √(ab)(xy)-------------(1)
Again as AM > GM
ax+by2 >2√axby
⇒ ax + by > 2 √abxy
From (1) & (2),
(ab + xy) (ax + by) > 4 abxy