If x + y + z = 9, then the value of (x - 4)3 + (y - 2)3 + (z - 3)3 - 3(x - 4)(y - 2)(z - 3) is?

Answer: Option C

$$\begin{array}{rl}& \underset{a^3}{\underset{\Downarrow }{{\left(x-4\right)}^3}}+\underset{b^3}{\underset{\Downarrow }{{\left(y-2\right)}^3}}+\underset{c^3-3abc}{\underset{\Downarrow }{{\left(z-3\right)}^3}}-3\left(x-4\right)\left(y-2\right)\left(z-3\right)\\ & \Rightarrow a+b+c=x-4+y-2+z-3\\ & \Rightarrow a+b+c=x+y+z-9\\ & \Rightarrow a+b+c=9-9\\ & \Rightarrow a+b+c=0\end{array}$$
$$\text{So, }{\left(x-4\right)}^3+{\left(y-2\right)}^3+$$     $${\left(z-3\right)}^3-$$   $$3\left(x-4\right)$$  $$\left(y-2\right)$$ $$\left(z-3\right)$$
$$\Rightarrow 0$$