conditional identity

Question

if a+b+c=0  prove that (a^2-bc) = (b^2-ca)=(c^2-ab)= -ab-bc-ca

Answer 1

if a+b+c=0 prove that (a^2-bc) = (b^2-ca)=(c^2-ab)= -ab-bc-ca LHS LHS LHS =(a^2-bc) =(b^2-ca) =(c^2-ab) =(a)(a)-bc =(b)(b)-ca =(c)(c)-ab =(-b-c)(a)-bc =(-a-c)(b)-ca =(-a-b)(c)-ab =-ab-ac-bc =-ab-bc-ca =-ac-bc-ab =-ab-bc-ca =RHS =-ab-bc-ca =RHS =RHS