Considering LHS
On further calculation
= (a + b + c) [(c – a) (c + a – 2b) – (b – c) (a + b – 2c)]
By multiplication
= (a + b + c) [c2 + ca – 2bc – ca – a2 + 2ab – ab – b2 + 2bc + ac + bc – 2c2]
By simplification
= (a + b + c) [- a2 – b2 – c2 + ab + bc + ac]
Taking –ve sign as common
= – (a + b + c) [a2 + b2 + c2 + ab + bc + ac]
We get
= – (a3 + b3 + c3 – 3abc)
= 3abc – a3 – b3 – c3
= RHS
Hence, it is proved.