" 9."[|x|x^(2)quad yz|],[yquad y^(2)quad zx|=(x-y)(y-z)(z-x)(xy+yz+zx)],[zquad z^(2)quad xy|]

[[x,x^(2),yzy,y^(2),zxz,z^(2),xy]]=(x-y)(y-z)(z-x)(xy+yz+zx)

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

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

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

xquad x ^ (2), y2yquad y ^ (2), 2xz, z ^ (2), xy] | = (xy) (yz) (zx) (xy + yz + 2x)

Show that: |[x, y ,z],[x^2, y^2, z^2], [yz, zx, xy ]|=(x-y)(y-z)(z-x).(xy+yz+zx)

By using properties of determinants , show that : {:|( x,x^(2) , yz) ,( y,y^(2) , zx ) ,( z , z^(2) , xy ) |:} =( x-y)(y-z) (z-x) (xy+yz+ zx)

Simplify- (x-y)/(xy)+(y-z)/(yz)+(z-x)/(zx)