Question

How to prove the identiy a 3 +b 3 +c 3 -3abc

Answer 1

(a+b+c)(a2+b2+c2-ab-bc-ca) 

= a^3+ab^2+ac^2-a^2b-abc-ca^2 + ba^2+b^3+bc^2-ab^2-b^2c-bca + ca^2+cb^2+c^3-cab-bc^2-c^2a 

= (a^3+b^3+c^3) + (ab^2-ab^2) + (ac^2-c^2a) + (-a^2b+ba^2) + (-abc-bca-cab) + (-ca^2+ca^2) + (bc^2-bc^2) + (-b^2c+c^2b) 

= a^3+b^3+c^3 -3abc