MCQ
If $a + b + c = 0$ then $\left(a^3+b^3+c^3\right)$ is:
- A$0$
- B$abc$
- C$2abc$
- ✓$3abc$
✓
Answer
Correct option: D.
$3abc$
$a+b+c=0$
$\Rightarrow a+b=-c$
$\Rightarrow(a+b)^3=(-c)^3$
$\Rightarrow a^3+b^3+3 a b(a+b)=-c^3$
$\Rightarrow a^3+b^3+3 a b(-c)=-c^3$
$\Rightarrow a^3+b^3+c^3=3 a b c$
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