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in Determinants by (47.9k points)

Prove that:

\(\begin{vmatrix}a + b + c&-c&-b\\[0.3em]-c&a + b+ c&-a\\[0.3em]-b&-a&c + a + b\end{vmatrix}\) = 2(a + b)(b + c)(c + a)

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Best answer

LHS =  \(\begin{vmatrix}a + b + c&-c&-b\\[0.3em]-c&a + b+ c&-a\\[0.3em]-b&-a&c + a + b\end{vmatrix}\) 

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