Question

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

Answer 1

Step-by-step explanation:

x+y=-z

y+z=-x

z+x=-y

(-z)^3+(-x)^3+(-y)^3-3(-x)(-y)(-z)=(-x-y-z)(x^2+y^2+z^2-xy-yz-zx)

=-(x+y+z)(x^2+y^2+z^2-xy-yz-zx)

(-z^3)+(-x)^3+(-y)^3+3xyz=0

(-z)^3+(-x)^3+(-y)^3=-3xyz

(x+y)^3+(y+z)^3+(z+x)^3=-3xyz