Factorise : `|(1,1,1),(x,y,z),(x^2,y^2,z^2)|`

Factorise : |(1,1,1),(x,y,z),(x^3,y^3,z^3)|

Find the value of : |(1+x,y,z),(x,1+y,z),(x,y,1+z)|

Factorise: xy+x+y+1

Factorise (x-y)^3+(y-z)^3+(z-x)^3

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

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

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

Show that |(x, x^(2),y+z),(y,y^(2),z+x),(z,z^(2),x+y)| = (y-z)(z-x)(x-y)(x+y+z) .

Resolve into factors : x^6+y^6+z^6-3x^2y^2z^2

Using properties of determinant show that : |((x+y)^2,zx,zy),(zx,(z+y)^2,xy),(zy,xy,(z+x)^2)|=2xyz(x+y+z)^3