Problem
ALG-B1-M11-P006 Zero sum
#6
★★☆☆☆ Level 2 of 5
Let \(a+b+c=0\). Prove \(a^3+b^3+c^3=3abc\).
Use the factorization of \(a^3+b^3+c^3-3abc\).
\(a^3+b^3+c^3-3abc=(a+b+c)(a^2+b^2+c^2-ab-bc-ca)=0\).
Strategy: recognize a special condition.