Question

If a + b + c = 0, then a³ + b³ + c³ = ?
(a) 0
(b) abc
(c) 2abc
(d) 3abc

Answer 1

(d) 3abc

$$\begin{gathered} a+b+c=0 \\ \Rightarrow a+b=-c \end{gathered}$$

$$\begin{gathered} \Rightarrow {\left(a+b\right)}^3={\left(-c\right)}^3 \\ \Rightarrow a^3+b^3+3ab\left(a+b\right)=-c^3 \\ \Rightarrow a^3+b^3+3ab\left(-c\right)=-c^3 \\ \Rightarrow a^3+b^3+c^3=3abc \end{gathered}$$