We have to prove the following determinant: $$\begin{vmatrix} a&b-c&c+b\\a+c&b&c-a\\a-b&b+a&c \end{vmatrix}=(a+b+c)(a^2+b^2+c^2)$$
I tried to solve it by expanding it, but it's getting too long.
2026-04-08 16:12:58.1775664778
Short method to solve determinant
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Actually I am new here so I don't know how to write determinants. So I solved this on my notebook. If any doubt please ask me.