If `x+y+z+w=0` then value of `x^3+y^3+z^3+w^3+3(y+z)(z+x)(x+y)=`

If x+y+z=8\ \ a n d\ \ \ x y+y z+z x=20 , find the value of x^3+y^3+z^3-3x y z

What is the value of ((x - y)^3 + (y - z)^3 + (z - x)^3)/(9(x - y)(y - z)(z - x)) ?

If x+y+z=0 show that x^3+y^3+z^3=3x y z .

Value of (x-y)^(3) +(y-z)^(3) +(z-x)^(3) is

If x + y + z = 0 , then what is (y+z-x)^(3) + (z+x-y)^(3) + (x+y-z)^(3) equal to ?

If x= a+ b, y = a omega + b omega^(2), z= a omega^(2) + b omega , then the value of x^(3) + y^(3) + z^(3) is equal to (where omega is imaginary cube root of unity)

If A=[(x,y,z),(y,z,x),(z,x,y)] and A^3=I_3 and xyz=2 and x+y+z gt 0 find the value of x^3+y^3+z^3 is

If [{:(x -y ,4),(z + 6 , x + y ):}] = [{:(8, w),(0,0):}] , then the value of (x + y + w + z) is

If x+y+z=0, then find (x+y)^(3)+(y+z)^(3)+(z+x)^(3)