Factorise`|[x,y,z],[x^(2),y^(2),z^(2)],[yz,zx,xy]|`

proof |[x,y,z],[x^(2),y^(2),z^(2)],[yz,zx,xy]| = |[1,1,1],[x^(2),y^(2),z^(2)],[x^(3),y^(3),z^(3)]|

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)

Factorise : 4xy -x^(2) - 4y^(2) + z^(2)

Factorise x^(2)-(y-z)^(2) .

Factorise : 16x^(2) - y^(2) + 4yz - 4z^(2)

Factorise : (v) x^(2) - 2xy + y^(2) - z^(2)

Prove that |{:(ax,,by,,cz),(x^(2),,y^(2),,z^(2)),(1,,1,,1):}|=|{:(a,,b,,c),(x,,y,,z),(yz,,xz,,xy):}|

Prove the identities: |[z, x, y],[ z^2,x^2,y^2],[z^4,x^4,y^4]|=|[x, y, z],[ x^2,y^2,z^2],[x^4,y^4,z^4]|=|[x^2,y^2,z^2],[x^4,y^4,z^4],[x, y, z]| =x y z (x-y)(y-z)(z-x)(x+y+z)

evaluate: |(0,xy^(2),xz^(2)),(x^(2)y,0,yz^(2)),(x^(2)z,zy^(2),0)|

Factorise : (vi) x^(2) - y^(2) - 2yz - z^(2)