If $(x-y)=3$, then what is the value of $\left(x^{3}-y^{3}-\right.$ $9 x y)$ ?

x – y = 3 On cubing both sides, (x – y)³ = 27 $\Rightarrow x^{3}-y^{3}-3 x y(x-y)=27$ $\Rightarrow x^{3}-y^{3}-9 x y=27$

Alternative:

Given that x – y = 3

Let y = 0

x = 3

$\Rightarrow x^{3}-y^{3}-9 x y$

$\Rightarrow(3)^{3}-0$

$=27$