Problem
ALG-B1-M10-P008 Zero sum
#8
★★☆☆☆ Level 2 of 5
Let \(a+b+c=0\). Prove that \(a^3+b^3+c^3=3abc\).
Use the identity for the sum of cubes.
\(a^3+b^3+c^3-3abc=(a+b+c)(a^2+b^2+c^2-ab-bc-ca)=0\). Hence \(a^3+b^3+c^3=3abc\).
Review of a key identity in a mixed context.