If `x+y+z=0` , then, `x^3+y^3+z^3+3\ x y z` is equal to (a) 0 (b) 6 `x y z` (c) 12 `x y z` (d) `x y z`

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

If x + y + z = 0 , then ( x + y - z)^(3) + ( y + z - x)^(3) + (z + x - y) ^(3) = k (xyz) , where k is equal to :

Value of [[x+y, z,z ],[x, y+z, x],[y, y, z+x]], where x ,y ,z are nonzero real number, is equal to x y z b. 2x y z c. 3x y z d. 4x y z

Value of [[x+y, z,z ],[x, y+z, x],[y, y, z+x]], where x ,y ,z are nonzero real number, is equal to x y z b. 2x y z c. 3x y z d. 4x y z

Value of |[x+y, z,z ],[x, y+z, x],[y, y, z+x]|, where x ,y ,z are nonzero real number, is equal to a. x y z b. 2x y z c. 3x y z d. 4x y z

Value of |[x+y, z,z ],[x, y+z, x],[y, y, z+x]|, where x ,y ,z are nonzero real number, is equal to a. x y z b. 2x y z c. 3x y z d. 4x y z

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

What should be added to x y+y z+z x to get x y-y z-z x ? -2x y-2y z-2z x (b) -3x y-y z-z x -3x y-3y z-3z x (d) 2x y+2y z+2z x

If x y z=0, then find the value of (a^x)^(y z)+(a^y)^(z x)+(a^z)^(x y)= (a)3 (b) 2 (c)1 (d) 0