ab(x² + y²) – xy(a² + b²)

= abx² + aby² – a²xy – b²xy

= abx² – a²xy + aby² – b²xy

= ax(bx – ay) + by(ay – bx)

= ax(bx – ay) – by(bx – ay)

= (bx – ay)(ax – by)

So we get,

ab(x² + y²) – xy(a² + b²) = (bx – ay)(ax – by)