alleryStart learning →If $a + b + c = 0$, what is the value of $a^3 + b^3 + c^3$?
- $3abc$
- $-3abc$
- $0$
- $abc$
Show answer and solution
Correct answer: A. $3abc$
The general identity $a^3+b^3+c^3 - 3abc = (a+b+c)(a^2+b^2+c^2-ab-bc-ca)$ collapses when $a+b+c = 0$: the RHS is zero, so $a^3+b^3+c^3 = 3abc$.
A frequent slip is to pick option A — that would require *all three* numbers to be zero, not just their sum.