证明：
$$
\begin{aligned}
& \left|\begin{array}{llll}
1 & 1 & 1 & 1 \\
a & b & c & d \\
a^2 & b^2 & c^2 & d^2 \\
a^4 & b^4 & c^4 & d^4
\end{array}\right| \\
= & (a-b)(a-c)(a-d)(b-c)(b-d)(c-d)(a+b+c+d)
\end{aligned}
$$
$\text{A.}$
$\text{B.}$
$\text{C.}$
$\text{D.}$