The simplification value of ( 3 + 1 ) ( 10 + 12 ) ( 12 - 2 ) ( 5 - 3 ) is = ?

Answer: Option C

$$\begin{array}{rl}& \left(\sqrt{3}+1\right)\left(10+\sqrt{12}\right)\left(\sqrt{12}-2\right)\left(5-\sqrt{3}\right)\\ & \Rightarrow \left(\sqrt{3}+1\right)\left(10+2\sqrt{3}\right)\left(2\sqrt{3}-2\right)\left(5-\sqrt{3}\right)\end{array}$$
$$\Rightarrow \left(\sqrt{3}+1\right)\times$$   $$2\left(5+\sqrt{3}\right)\times$$   $$2\left(\sqrt{3}-1\right)$$  $$\left(5-\sqrt{3}\right)$$
$$\begin{array}{rl}& \Rightarrow 4\left(\sqrt{3}+1\right)\left(\sqrt{3}-1\right)\left(5+\sqrt{3}\right)\left(5-\sqrt{3}\right)\\ & \Rightarrow 4\left[{\left(\sqrt{3}\right)}^2-1^2\right]\left[{\left(5\right)}^2-{\left(\sqrt{3}\right)}^2\right]\\ & \Rightarrow 4\times 2\times 22\\ & \Rightarrow 176\end{array}$$