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If $a + b + c = 0$, what is the value of $a^3 + b^3 + c^3$?
A$3abc$
B$-3abc$
C$0$
D$abc$
Answer & 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.
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