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

Prove that `|{:(x,y,z),(x^2,y^2,z^2),(yz,zy,xy):}|=|{:(1,1,1),(x^2,y^2,z^2),(x^3,y^3,z^3):}|=(y-z)(z-x)(x-y)(yz+zy+xy)`

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`Delta=|{:(x,y,z),(x^2,y^2,z^2),(yz,zy,xy):}|=1/(xyz)|{:(x^2,y^2,z^2),(x^3,y^3,z^3),(xyz,xyz,xyz):}|=(xyz)/(xyz)|{:(x^2,y^2,z^2),(x^3,y^3,z^3),(1,1,1):}|`
`C_1toC_2toC_1,C_3toC_3-C_1`
`|{:(1,0,0),(x^2,y^2-x^2,z^2-x^2),(x^2,y^2-x^2,z^2-x^2):}|`
`=(y-x)(z-x)|{:(y+x,z+x),(y^2+xy+x^2,z^2+zx+x^2):}|`
`(y-z)(z-x)(z-y)[(y+x)(x+y+z)-(y^2+xY+x^2)]`
`=(x-y)(y-z)(xy+yz+zx)`
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