The value of ( 3 + 2 2 )^ - 3 + ( 3 - 2 2 )^ - 3 = ?

Answer: Option D

$$\begin{array}{rl}& {\left(3+2\sqrt{2}\right)}^{-3}+{\left(3-2\sqrt{2}\right)}^{-3}\\ & ={\left(\frac{1}{3+2\sqrt{2}}\right)}^3+{\left(\frac{1}{3-2\sqrt{2}}\right)}^3\end{array}$$
  $$={\left(\frac{1}{\left(3-2\sqrt{2}\right)}\times \frac{3+2\sqrt{2}}{3+2\sqrt{2}}\right)}^3+$$      $${\left(\frac{1}{\left(3+2\sqrt{2}\right)}\times \frac{3-2\sqrt{2}}{3-2\sqrt{2}}\right)}^3$$
$$\begin{array}{rl}& ={\left(\frac{3-2\sqrt{2}}{9-8}\right)}^3+{\left(\frac{3+2\sqrt{2}}{9-8}\right)}^3\\ & ={\left(3-2\sqrt{2}\right)}^3+{\left(3+2\sqrt{2}\right)}^3\\ & a=3-2\sqrt{2}\\ & b=3+2\sqrt{2}\\ & \left[\because a^3+b^3=\left(a+b\right)\left(a^2+b^2-ab\right)\right]\\ & =\left(3-2\sqrt{2}+3+2\sqrt{2}\right)\left(17+17-1\right)\\ & =\left(6\right)\left(33\right)\\ & =198\end{array}$$