Without expanding the determinant, prove that $\begin{vmatrix} a &a^2 &bc \\ b &b^2 &ca \\ c &c^2 &ab \end{vmatrix}\; = \; \begin{vmatrix} 1 & a^2 & a^3 \\ 1 & b^2 & b^3 \\ 1 & c^2 & c^3 \end{vmatrix}$

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