Question

\(\begin{vmatrix} a & b & c \\[0.3em] a - b &b - c &c - a \\[0.3em] b + c & c + a &a + b \end{vmatrix}\) = a³ + b³ + c³ - 3abc.

Answer 1

From L.H.S. 

On applying C₁ → C₁ + C₂ + C₃

Take (a + b + c) common from C₁

On applying R₃ → R₃ - 2R₁

Here, L.H.S. = R.H.S.

Hence proved.