[R₁’ = xR₁ & R₂’ = yR₂]

[R₁’ = R₁ + R₂ - R₃]

= (1/xy)[0 + 0 + (ax² + 2bxy + cy²){by(bx + cy) - cy(ax + by)}[expansion by first row] .

= (1/xy)( ax² + 2bxy + cy²)(b²xy + bcy² - acxy - bcy²)

= (b² - ac)(ax² + 2bxy + cy²)