\( P= \dfrac{{x\sqrt x + y\sqrt y }}{{\sqrt x + \sqrt y }} - {\left( {\sqrt x - \sqrt y } \right)^2}\)
\( P= \dfrac{{(\sqrt x)^3 + (\sqrt y)^3 }}{{\sqrt x + \sqrt y }} - {\left( {\sqrt x - \sqrt y } \right)^2}\)
\(P = \dfrac{{\left( {\sqrt x + \sqrt y } \right)\left( {x - \sqrt {xy} + y} \right)}}{{\sqrt x + \sqrt y }} \)\(- \left( {x - 2\sqrt {xy} + y} \right)\)
\(P=x-\sqrt{xy} +y-x+2\sqrt{xy}-y\)
\(P=\sqrt{xy}\)
