Verify that `x^(3)+y^(3)+z^(3)-3xyz=(1)/(2)(x+y+z)[(x-y)^(2)+(y-z)^(2)+(z-x)^(2)]`

verify that x^(3)+y^(3)+z^(3)-3xyz=(1)/(2)(x+y+z)[(x-y)^(2)+(y-z)^(2)+(z-a)^(2)]

Prove that x^(3)+y^(3)+z^(3)-3xyz=(1)/(2)(x+y+z)[(x-y)^(2)+(y-z)^(2)+(z-x)^(2)]

Verify that x3+y3+z3-3xyz=1/2(x+y+z)[(x-y)2+(y-z)2+(z-x)2]

Find ((x^(2)-y^(2))^(3) + (y^(2) -z^(2))^(3)+ (z^(2) -x^(2))^(3))/((x-y)^(3) + (y-z)^(3) + (z-x)^(3))

Simplify: ((x^(2)-y^(2))^(3) + (y^(2) - z^(2))^(3) + (z^(2) -x^(2))^(3))/((x-y)^(3) + (y-z)^(3) + (z-x)^(3))

If x + y + z = xyz , prove that (3x -x^(3))/ (1-3x^(2)) + (3y -y^(3))/(1- 3y^(2)) +(3z -z^(3))/(1- 3z^(2)) = (3x -x^(3))/(1-3x)^(2) * (3y- y^(3))/(1-3x)^(2)* (3z- z^(3))/(1-3z)^(2) .

The value of the expression ((x ^(2) - y ^(2)) ^(3) + ( y ^(2) - z ^(2)) ^(3) + (z ^(2) - x ^(2)) ^(3))/((x - y) ^(3) + ( y - z) ^(3) + (z - x ) ^(3)) is

Show that |(x,y,z),(x^(2),y^(2),z^(2)),(x^(3),y^(3),z^(3))|=xyz (x-y) (y-z) (z-x)