Evaluate $\Delta=\left\lvert\matrix{ 1 & x & yz \\ 1 & y & zx \\ 1 & z & xy }\right\rvert$
The answer of the above question is $(x-y)(y-z)(z-x)$.
But will solving I get stuck to $-yx^2+zx^2+xy^2-xz^2-zy^2-yz^2 $.
Please help me to solve the above problem