Question

Prove that \(\begin{vmatrix} 1 & a + b & a^2 + b^2 \\[0.3em] 1& b + c & b^2 + c^2 \\[0.3em] 1 &c + a &c^2 + a^2 \end{vmatrix}\)= (a + b)(b - c)(c - a)

Answer 1

(a - b)(c - a).1(a + b - c - a) = (a - b)(b - c)(c - a) = RHS