prove that determinant ![\left[\begin{array}{ccc}a&b&c\\bc&ca&ab\\b+c&c+a&a+b\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Da%26amp%3Bb%26amp%3Bc%5C%5Cbc%26amp%3Bca%26amp%3Bab%5C%5Cb%2Bc%26amp%3Bc%2Ba%26amp%3Ba%2Bb%5Cend%7Barray%7D%5Cright%5D "\left[\begin{array}{ccc}a&b&c\\bc&ca&ab\\b+c&c+a&a+b\end{array}\right]")
is equal to (a+b+c)(a-b)(b-c)(c-a)
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