Question

Prove that :

\(\begin{vmatrix}y + z&x&y\\[0.3em]z + x&z&x\\[0.3em]x+ y&y&z\end{vmatrix}\) = (x + y + z)(x - z)²

Answer 1

= (x + y + z)[0 - 0 + (x - z)(x - z)]

= (x + y + z)(x - z)² = RHS.