Prove that |(y + z,x,y),(z + x,z,x),(x + y,y,z)| = (x + y + z)(x - z)^2

Question

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

Answer 1

LHS

= (x + y + z)(x - z)² 

= RHS