Various proofs of important algebraic identity: a^{3}+b^{3}+c^{3}-3abc

We know the following factorization: $latex a^{3}+b^{3}+c^{3}-3abc= (a+b+c)(a^{2}+b^{2}+c^{2}-ab-bc-ca)$ Proof 1: Let a, b, c be roots of a polynomial P(X) Then by fundamental theorem of algebra $l…