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Prove that |{:( (a-x)^2,,(a-y)^2,,(a-z)^...

Prove that `|{:( (a-x)^2,,(a-y)^2,,(a-z)^2),((b-x)^2,,(b-y)^2,,(b-z)^2),((c-x)^2,,(c-y)^2,,(c-z)^2):}|`= `|{:((1+a x)^2,,(1+b x)^2,,(1+c x)^2),((1+a y)^2,,(1+b y)^2,,(1+c y)^2),((1+a z)^2,,(1+b z)^2,,(1+c z)^2):}|`=2(b-c)(c-a)(a-b)*(y-z)(z-x)(x-y).`

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