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.