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