If pq(p + q) = 1, then the value of 1p^3q^3 - p^3 - q^3 , is equal to?

Answer: Option C

$$\begin{array}{rl}& pq\left(p+q\right)=1\\ & \Rightarrow p+q=\frac{1}{pq}\\ & \text{Cubing both side}\\ & \Rightarrow p^3+q^3+3pq\left(p+q\right)=\frac{1}{p^3{q}^3}\\ & \text{Puting the value of }pq=\frac{1}{\left(p+q\right)}\\ & \Rightarrow \frac{1}{p^3{q}^3}-p^3-q^3=\left(\frac{3}{p+q}\right)\left(p+q\right)\\ & \Rightarrow \frac{1}{p^3{q}^3}-p^3-q^3=3\end{array}$$