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

Using the 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)

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

Using the properties of determinants, show that: abs((x,x^2,yz),(y,y^2,xz),(z,z^2,xy))=(x−y)(y−z)(z−x)(xy+yz+zx)

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

Using the properties of determinants, show that : |[[x^2, y^2, z^2],[yz, zx, xy],[x,y,z]]|= (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)

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)

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)) .