If xy(x + y) = m, then the value of x³ + y³ + 3m is?

Solution(By Examveda Team)

$$\eqalign{ & xy\left( {x + y} \right) = m \cr & {\text{find }}{x^3} + {y^3} + 3m \cr & xy\left( {x + y} \right) = m\, . . . . . (i) \cr & \left( {x + y} \right) = \frac{m}{xy} \cr &{\text{Cubing both side}} \cr & \Rightarrow {x^3} + {y^3} + 3.xy\left( {x + y} \right) = \frac{{{m^3}}}{{{x^3}{y^3}}} \cr & {\text{From equation (i)}} \cr & \Rightarrow {x^3} + {y^3} + 3.m = \frac{{{m^3}}}{{{x^3}{y^3}}} \cr & \Rightarrow {x^3} + {y^3} + 3m = \frac{{{m^3}}}{{{x^3}{y^3}}} \cr} $$