Question

If x+y+z = 0 then {(y - z - x )/2}^3 +{(z - x -y)/2} ^3+{(x -y -z)/2}^3 equal to what

Answer 1

Answer:

-3yz(y+z)

Step-by-step explanation:

x+y+z=0

y=-z-x

z=-x-y

x=-y-z

therefore,{(y-z-x)/2}^3={(y+y)/2}^3=y^3

similarly,{(z-x-y)/2}^3=z^3

{(x-y-z)/2}^3=x^3

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

x^3+y^3+z^3=0-3xy*0-3yz*0-3yz(y+z)=-3yz(y+z)