Using properties of determinants, prove the following: `|[1,x,x^2],[x^2, 1,x],[x,x^2,1]|=(1-x^3)^2`

Using properties of determinants prove the following. abs[[1,x,x^2],[x^2,1,x],[x,x^2,1]]=(1-x^3)^2

Prove the following : [[1,x,x^2],[x^2,1,x],[x,x^2,1]]=(1-x^3)^2

Using properties of determinants, prove the following |[x,x+y,x+2y],[x+2y,x,x+y],[x+y,x+2y,x]|=9y^2(x+y)

Using properties of determinants, prove the following |[x,x+y,x+2y],[x+2y,x,x+y],[x+y,x+2y,x]|=9y^2(x+y)

By using properties of determinants, show that : |[1,x,x^2],[x^2,1,x],[x,x^2,1]| = (1-x^3)^2

By using properties of determinants. Show that: |[1,x,x^2],[x^2, 1,x],[x,x^2, 1]|=(1-x^3)^2

Using properties of determinants, prove the following: |[x,x^2,1+px^3],[y,y^2,1+py^3],[z,z^2,1+pz^3]|=(1+pxyz)(x-y)(y-z)(z-x)

Using properties of determinants, prove the following: |[x,x^2,1+px^3],[y,y^2,1+py^3],[z,z^2,1+pz^3]|=(1+pxyz)(x-y)(y-z)(z-x)