If x ,y ,z are all different and $$\begin{gathered} \left|\begin{array}{ccc}{x}^3& (x+p{)}^3 & (x-p{)}^3\\ y^3& (y+p{)}^3& (y-p{)}^3\\ z^3& (z+p{)}^3& (z-p{)}^2\end{array}\right| =0, prove that \\ {p}^2 ( x +y + z) = 3xyz \end{gathered}$$