MCQ
If $a + b + c = 0$ then $a^3+ b^3 + c^3$ is equal to
  • $3\text{abc}$
  • B
    $\frac{3}{\text{abc}}$
  • C
    $3\text{a}^3\text{b}^3\text{c}^3$
  • D
    $\text{Zero}$

Answer

Correct option: A.
$3\text{abc}$

Using $a^3 + b^3 + c^3 - 3abc = (a + b + c)(a^2 + b^2 + c^2 - ab - bc - ca)$
Using $a^3 + b^3 + c^3 - 3abc = 0 \times (a^2 + b^2 + c^2 - ab - bc - ca)$
Using $a^3 + b^3 + c^3 = 3abc$
Here if $a + b + c$ is $0$ then answer will be $3abc$

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