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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

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    Hint: Remember that $x^2 - y^2 = (x+y)(x-y)$.2012-09-18
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    Also, you have the wrong sign on $yz^2$. It is supposed to be plus, and you have minus. An easy way to notice that something is wrong is to see that you have two plus terms and four minus terms, but it should be three of each.2012-09-18

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