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|[y^(2)z^(2),yz,y+z],[z^(2)x^(2),zx,z+x]...

|[y^(2)z^(2),yz,y+z],[z^(2)x^(2),zx,z+x],[x^(2)y^(2),xy,x+y]|=0

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|(x^(2),y^(2)+z^(2),yz),(y^(2),z^(2)+x^(2),zx),(z^(2),x^(2)+y^(2),xy)| is divisible by

Using properties of determinants, prove that |{:(y^2z^2,yz,y+z),(z^2x^2,zx,z+x),(x^2y^2,xy,x+y):}|=0

Prove that |(x^(2),x^(2)-(y-z)^(2),yz),(y^(2),y^(2)-(z-x)^(2),zx),(z^(2),z^(2)-(x-y)^(2),xy)|=(x-y)(y-z)(z-x)(x+y+z)(x^(2) + y^(2) + z^(2)) .

yz-x^(2)quad zx-y^(2)quad xy-z^(2)| Prove that det[[yz-x^(2),zx-y^(2),xy-z^(2)zx-y^(2),xy-z^(2),yz-x^(2)xy-z^(2),yz-x^(2),zx-y^(2)]] is divisible by (x+y+z), and hence find the quotient.

|[1/x,1/y,1/z],[x^(2),y^(2),z^(2)],[yz,zx,xy]|

Prove that |{:(x^(2),,x^(2)-(y-z)^(2),,yz),(y^(2),,y^(2)-(z-x)^(2),,zx),(z^(2),,z^(2)-(x-y)^(2),,xy):}| =(x-y) (y-z) (z-x)(x+y+z) (x^(2)+y^(2)+z^(2))

Prove that |{:(x^(2),,x^(2)-(y-z)^(2),,yz),(y^(2),,y^(2)-(z-x)^(2),,zx),(z^(2),,z^(2)-(x-y)^(2),,xy):}| =(x-y) (y-z) (z-x)(x+y+z) (x^(2)+y^(2)+z^(2))

Prove that quad det ([yx-x^(2),zx-y^(2),xy-z^(2)zx-y^(2),xy-z^(2),yz-x^(2)xy-z^(2),yz-x^(2),zx-y^(2)]) is divisible by (x+y+z) and hence find the quotient.

proof |[x,y,z],[x^(2),y^(2),z^(2)],[yz,zx,xy]| = |[1,1,1],[x^(2),y^(2),z^(2)],[x^(3),y^(3),z^(3)]|

Which of the following are possible solutions of |(y^2+z^2,xy,xz),(xy,z^2+x^2,yz),(zx,zy,x^2+y^2)|=8 are (x,y,z)=