Given that

Applying R_{1} →xR_{1}, R_{2} → yR_{2} ,R_{3} → zR_{3} to Δ and dividing by xyz, we get

Taking common factors x, y, z from C_{1, }C_{2 }and C_{3} respectively, we get

Applying C_{2} → C_{2}– C_{1}, C_{3 }→ C_{3}– C_{1}, we have

Taking common factor (x + y + z) from C_{2} and C_{3}, we have

Applying C_{2} → (C_{2 }+ 1/yC_{1}) and C_{3} → C_{3} + 1/zC_{1}, we get

Finally expanding along R_{1}, we have

Δ = (x + y + z)^{2} (2yz) [(x + z) (x + y) – yz]

= (x + y + z)^{2} (2yz) (x^{2 } + xy + xz)

= (x + y + z)^{3}(2xyz)