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We need to prove the determinant: \[ D = \begin{vmatrix} b+c & a & a \\ c & c+a & a \\ b & a & a+b \end{vmatrix} \] ### Step 1: Expand the determinant using cofactor expansion along the first row Expanding along the first row: \[ D = (b+c) \begin{vmatrix} c+a & a \\ a & a+b \end{vmatrix} - a \begin{vmatrix} c & a \\ b & _________ _____ _______ ______ ________ ___ _____ ________ __________ ______ ______.
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