Applying AM - GM inequality, we have
\(\frac{ab+xy}{2}≥\sqrt{ab.xy}\) ⇒ (ab + xy) ≥ 2\(\sqrt{ab.xy}\) ......(i)
and \(\frac{(ab+xy)}{2}≥\sqrt{ab.xy}\) ⇒ (ab + xy) ≥ 2\(\sqrt{ab.xy}\) ......(ii)
Multiplying (i) and (ii), we get
(ab + xy) (ax + by) > 4\(\sqrt{abxy}\sqrt{abxy}\) ⇒ (ab + xy) (ax + by) > 4 abxy.