Using properties of determinants prove that:

Using properties of determinants prove that: $\begin{vmatrix} x & x(x^2 + 1) & x + 1 \\\\ y & y(y^2 + 1) & y + 1 \\\\ z & z(z^2 + 1) & z + 1 \end{vmatrix} = (x - y)(y - z)(z - x)(x + y + z)$