Prove that `|[x+y+2z,x,y],[z,y+z+2x,y],[z,x,z+x+2y]|= 2(x+y+z)^(3)`

Prove that |{:(,x+y+2z,x,y),(,z,y+z+2z,y),(,z,x,z+x+2y):}|=2(x+y+z)^(3) .

|[x,1,y+z],[y,1,z+x],[z,1,x+y]|=

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

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

|[1, x, x^2 ],[1, y, y^2],[1, z, z^2]|=

|(x, 4, y+z),(y, 4, z+x),(z, 4, x+y)|=

The value of |(x+y,y+z,z+x),(x,y,z),(x-y,y-z,z-x)|=

Without expanding prove that Delta ={:|( x+y,y+z,z+x) ,( z,x,y),( 1,1,1) |:} =0

using properties of determinant prove that {:[( x,x^(2) , 1+ px^(3) ),( y,y^(2) , 1+ py^(2)),( z,z^(2) , 1+pz^(2)) ]:} =( 1+pxyz ) ( x-y) ( y-z ) (z-x) , where p is any scalar .

If Delta= [[0 , x , -y ],[-x , 0 , z],[ y , -z , 0 ]] then