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已在math.stackexchange.com/questions/4900084/leading-term-of-difference-of-two-products提问但无回復
$n\ge1$，设
$$P_n(x)=\prod_{\substack{\mu_1,\dots,\mu_n\in\{\pm1\}\\\mu_1\dots\mu_n=1}}(x-(\mu_1{x_1}+\dots+\mu_n{x_n}))$$
$$Q_n(x)=\prod_{\substack{\mu_1,\dots,\mu_n\in\{\pm1\}\\\mu_1\dots\mu_n=-1}}(x-(\mu_1{x_1}+\dots+\mu_n{x_n}))$$
则 $Q_n-P_n$ 的首项是 ${x_1\dots x_n}2^n(n-1)!x^{2^{n-1}-n}$?
如\begin{gather*}
Q_1=(x+x_1)\\P_1=(x-x_1)\\Q_1-P_1=2x_1
\end{gather*}
\begin{gather*}
Q_2=(x-x_1+x_2)(x+x_1-x_2)\\P_2=(x+x_1+x_2)(x-x_1-x_2)\\Q_2-P_2=4x_1x_2
\end{gather*}
\begin{gather*}
Q_3=(x+x_1+x_2+x_3)(x-x_1-x_2+x_3)(x-x_1+x_2-x_3)(x+x_1-x_2-x_3)\\
P_3=(x-x_1+x_2+x_3)(x+x_1-x_2+x_3)(x+x_1+x_2-x_3)(x-x_1-x_2-x_3)\\
Q_3-P_3=16 x x_1 x_2 x_3
\end{gather*}
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