Prove the following identities:

Applying, R₂→R₂ – R₁, and R₃→R₃ – R₁

= (b – a)(c – a)[((b + a – c))(c² + a² + ac) – (b² + a² + ab)(c² + a² + ac)]

= – (a – b)(c – a)(b – c)(a² + b² + c²)

= R.H.S

Hence, proved.