If $a + b + c = 0$, then $a^{3}+b^{3}+c^{3}$ equals

Question

Aicharya · Accepted Answer

Identity: $a^{3}+b^{3}+c^{3} - 3abc = (a+b+c)(a^{2}+b^{2}+c^{2}-ab-bc-ca)$. If $a+b+c=0$, the right side is $0$, so $a^{3}+b^{3}+c^{3}=3abc$.

Solution