If ab(a + b) = 1, then what is the value of 1a^3b^3 - a^3 - b^3?

Answer: Option C

$$\begin{array}{rl}& \because ab\left(a+b\right)=1\\ & \Rightarrow a+b=\frac{1}{ab}.......\left(\text{i}\right)\\ & \text{On cubing both sides}\\ & \Rightarrow a^3+b^3+3ab\left(a+b\right)=\frac{1}{a^3{b}^3}\\ & \Rightarrow a^3+b^3+3ab\times \frac{1}{ab}=\frac{1}{a^3{b}^3}\left(\text{from equation }\left(\text{i}\right)\right)\\ & \Rightarrow \frac{1}{a^3{b}^3}-a^3-b^3=3\end{array}$$