Prove that : $$\left| \begin {array} c (2bc-a^2) & c^2 & b^2 \\ c^2 & (2ac-b^2) & a^2 \\ b^2 & a^2 & (2ab-c^2) \end{array} \right| =D^2.$$
Where $$D= \left| \begin {array} c a& b &c \\ b & c & a \\ c& a & b \end {array} \right|.$$
It is my problem .I simply expand it but it made complex so I think we need to use several operations.
Write $D^2$ as $ \begin{vmatrix} b & c & a\\ c & a & b\\ a & b & c \end{vmatrix} \times \begin{vmatrix} c & a & b\\ b & c & a\\ -a & -b & -c \end{vmatrix} $
Proving that $D$ is equivalent to each of the above two determinants is a trivial exercise