The third proportional of the following numbers (x - y)2, (x2 - y2) = ?

Answer: Option C

$$\begin{array}{rl}& \text{Let,}\\ & a={\left(x-y\right)}^2,\\ & b=\left(x^2-y^2\right)\text{and}\\ & c\text{be}\text{the}\text{third}\text{proportional}\\ & \text{Therefore}a:b::b:c\\ & i.e.c=\frac{b^2}{a}\\ & \Rightarrow c=\frac{{\left(x^2-y^2\right)}^2}{\left(x-y\right)}\\ & =\frac{{\left(x-y\right)}^2{\left(x+y\right)}^2}{\left(x-y\right)}\\ & =\left(x-y\right){\left(x+y\right)}^2\end{array}$$