Question

hala everyone!!
plz answer me in a proper and short way!!

If X + Y + Z = 0 . Show that x cube + y cube + z cube equals to 3 xyz

Answer 1

hope this helps...!!

Answer 2

x+y+z=0
x+y= -z
Cubing both sides
${(x + y)}^{3} = - {z}^{3} \\ {x}^{3} + {y}^{3} + 3xy(x + y) = - {z}^{3} \\ {x}^{3} + {y}^{3} + 3xy( - z) = - {z}^{3} \\ {x}^{3} + {y}^{3} + {z}^{3} - 3xyz = 0 \\ {x}^{3} + {y}^{3} + {z}^{3} = 3xyz$
HOPE IT HELPS ✌️✌️