If a + b + c = 0, then the value of (a + b - c)2 + (b + c - a)2 + (c + a - b)2 is?

Answer: Option C

$${\left(a+b-c\right)}^2\text{ + }{\left(b+c-a\right)}^2$$     $$\text{ + }{\left(c+a-b\right)}^2$$
$$\begin{array}{rl}& \Rightarrow a+b+c=0\left(\text{ Given}\right)\\ & \Rightarrow a+b=-c\\ & \Rightarrow b+c=-a\\ & \Rightarrow a+c=-b\end{array}$$
$$\Rightarrow {\left(a+b-c\right)}^2+{\left(b+c-a\right)}^2$$      $$+{\left(c+a-b\right)}^2$$
$$\begin{array}{rl}& \Rightarrow {\left(-c-c\right)}^2\text{ + }{\left(-a-a\right)}^2\text{ + }{\left(-b-b\right)}^2\\ & \Rightarrow {\left(-2c\right)}^2\text{ + }{\left(-2a\right)}^2\text{ + }{\left(-2b\right)}^2\\ & \Rightarrow 4c^2+4a^2+4b^2\\ & \Rightarrow 4\left(a^2+b^2+c^2\right)\end{array}$$