[C₁’ = C₁ + C₂ + C₃]

[C₁’ = C₁/(x + y + z)]

[transforming row and column]

[C₁’ = C₁ - C₂ & C₂’ = C₂ - C₃]

= (x + y + z)[0 + 0 + ( - x - 2y)( - y - 2z) - ( - x + y)(2y + z)] [expansion by first row]

= (x + y + z)(xy + 2y² + 2xz + 4yz + 2xy - 2y² + xz - yz)

= (x + y + z)(3xy + 3yz + 3xz)

= 3(x + y + z)(xy + yz + zx)