If x + y = z, then the expression x³ + y³ - z³ + 3xyz will be equal to?

Solution (By Examveda Team)

$$\eqalign{ & x + y = z \cr & x + y - z = 0 \cr & {\text{If }}a + b + c = 0 \cr & {\text{then }}{a^3} + {b^3} + {c^3} - 3abc = 0 \cr & \Rightarrow {x^3} + {y^3} - {z^3} = - 3xyz \cr & \therefore {x^3} + {y^3} - {z^3} + 3xyz = 0 \cr & \Rightarrow 3xyz - 3xyz = 0 \cr} $$