Question

Prove that \(\begin{vmatrix} a^2& bc & ac + c^2 \\[0.3em] a^2 + ab & b^2 &ac\\[0.3em] ab &b^2 + bc & c^2 \end{vmatrix}\) = 4a²b²c²

Answer 1

expand along c₁

= 2ab²c{1 x (a - c)c + c(a + c)}

= 2ab²c{ac - c² + ac + c²} = 2ab²c x 2ac

= 4a²b²c².