$\begin{array}{l} ab\left( {{x^2} + {y^2}} \right) + xy\left( {{a^2} + {b^2}} \right) = ab\\ \Leftrightarrow ab\left[ {{{\left( {x + y} \right)}^2} - 2xy} \right] + xy\left( {{a^2} + {b^2}} \right) = ab\\ \Leftrightarrow ab{\left( {x + y} \right)^2} - 2xyab + xy\left( {{a^2} + {b^2}} \right) = ab\\ \Leftrightarrow ab + xy\left( {{a^2} + {b^2} - 2ab} \right) = ab\\ \Leftrightarrow xy{\left( {a - b} \right)^2} = 0\\ \Leftrightarrow a = b\left( {x,y \ne 0} \right) \end{array}$
