`|(y^(2)z^(2),yzx,y+z),(z^(2)x^(2),zx,z+x),(x^(2)y^(2),xy,x+y)|=0`

prove that: |(y^(2)z^(2),yz,y+z),(z^(2)x^(2),zx,z+x),(x^(2)y^(2),xy,x+y)|=0

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

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))

x(y^(2)-z^(2))+y(z^(2)-x^(2))+z(x^(2)-y^(2)) is divisible by

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.

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)=

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.

Prove that : |{:((y+z)^(2),x^(2),x^(2)),(y^(2),(x+z)^(2),y^(2)),(z^(2),z^(2),(x+y)^(2)):}|=2xyz (x+y+z)^(3)