If p3 - q3 = (p - q) (p - q)2 - xpq, then find the value of x :

Answer: Option B

$$p^3-q^3=\left(p-q\right)$$   $$\left\{{\left(p-q\right)}^2-xpq\right\}$$
$$\Rightarrow \left(p-q\right)\left(p^2+q^2+pq\right)$$     $$=\left(p-q\right)$$   $$\left\{{\left(p-q\right)}^2-xpq\right\}$$
$$\left\{\because a^3-b^3=\left(a-b\right)\left(a^2+ab+b^2\right)\right\}$$
By cancelling same terms of both sides
$$\Rightarrow p^2+q^2+pq=p^2+q^2$$     $$-2pq-xpq$$   $$\left\{{\left(a-b\right)}^2=a^2+b^2-2ab\right\}$$
$$\begin{array}{rl}& \Rightarrow 3pq=-xpq\\ & \Rightarrow x=-3\end{array}$$