[x-y-z,2x,2x],[2y,y-z-x,2y],[2z,2z,z-x-y]=......

By using properties of determinants, show that : |[x+y+2z,x,y],[z,y+z+2x,y],[z,z,z+x+2y]| = 2(x+y+z)^3

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

By using properties of determinants, prove that |[x+y+2z,x,y],[z,y+z+2x,y],[z,x,z+x+2y]|=2(x+y+z)^3

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: |(2y, y-z-x,2y),(2z,2z, z-x-y),( x-y-z,2x,2x)|=(x+y+z)^3

Prove: |(2y, y-z-x,2y),(2z,2z, z-x-y),( x-y-z,2x,2x)|=(x+y+z)^3

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

Prove that |[x,x^(2),x^(4)],[y,y^(2),y^(4)],[z,z^(2),z^(4)]|=xyz(x-y)(y-z)(z-x)(x+y+z)

x-y+z=1 2x+y-z=2 x-2y-z=4