Using properties of determinants, prove that
`|{:(x,y,z),(x^(2),y^(2),z^(2)),(y+z,z+x,x+y):}|=(x-y)(y-z)(z-x)(x+y+z)`

Prove that : =|{:(1,1,1),(x,y,z),(x^(2),y^(2),z^(2)):}|=(x-y)(y-z)(z-x)

Prove that : |{:(1,1,1),(x,y,z),(x^(3),y^(3),z^(3)):}|=(x-y)(y-z)(z-x)(x+y+z)

Using properties of determinants, prove that |(a+x, y, z),(x, a+y, z),(x, y,a+z)|=a^2(a+x+y+z)

Using properties of determinats prove that : |(x,x(x^(2)+1),x+1),(y,y(y^(2)+1),y+1),(z,z(z^(2)+1),z +1)|=(x-y)(y-z)(z-x)(x+y+z)

By using properties of determinants. Show that: |[x,x^2,y z],[ y, y^2,z x],[ z, z^2,x y]|=(x-y)(y-z)(z-x)(x y+y z+z x)

Prove that : |{:(1,x,x^(3)),(1,y,y^(3)),(1,z,z^(3)):}| =(x-y)(y-z)(z-x)(x+y+z)

Using properties of determinants, prove that |[a+x,y,z],[x,a+y,z],[x,y,a+z]|=a^2(a+x+y+z)

Using properties of determinant prove that: |[1,x+y, x^2+y^2],[1, y+z, y^2+z^2],[1, z+x, z^2+x^2]|= (x-y)(y-z)(z-x)

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)

Prove that : |{:(1,x,yz),(1,y,zx),(1,z,xy):}|=(x-y)(y-z)(z-x)