计算 $D_n=\left|\begin{array}{cccc}
1+x_1^2 & x_1 x_2 & \cdots & x_1 x_n \\
x_2 x_1 & 1+x_2^2 & \cdots & x_2 x_n \\
\vdots & \vdots & & \vdots \\
x_n x_1 & x_n x_2 & \cdots & 1+x_n^2
\end{array}\right| .$
$\text{A.}$
$\text{B.}$
$\text{C.}$
$\text{D.}$
$\text{E.}$
$\text{F.}$