Calculate the determinant of the matrix, which is obtained by crossing out crossing out columns i and j.
$$ \left(\begin{array}{ccccc} 1 & x_{1} & \cdots & x_{1}^{n} & x_{1}^{n+1} \\ 1 & x_{2} & \cdots & x_{2}^{n} & x_{2}^{n+1} \\ \vdots & \vdots & \vdots & \vdots \\ 1 & x_{n} & \cdots & x_{n}^{n} & x_{n}^{n+1} \end{array}\right) $$