$\begin{array}{1 1} 9y^2(x+y) \\ 9x^2(x+y) \\ y^2(x+y) \\ x^2(x+y) \end{array} $

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Using properties of determinants,prove the following $\begin{vmatrix}x& x+y & x+2y\\x+2y & x & x+y\\x+y & x+2y & x\end{vmatrix}=9y^2(x+y)$

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