If a(x + y) = b(x - y) = 2ab, then the value of 2(x2 + y2) is?

Answer: Option D

$$\begin{array}{rl}& a\left(x+y\right)=b\left(x-y\right)=2ab\\ & x+y=2b\\ & \text{On squraing both side}\\ & \Rightarrow x^2+y^2+2xy=4b^2.....(i)\\ & \Rightarrow b\left(x-y\right)=2ab\\ & \Rightarrow x-y=2a\\ & \text{On squraing both side}\\ & \Rightarrow x^2+y^2-2xy=4a^2.....(ii)\\ & \text{Add equation (i) and (ii)}\\ & \Rightarrow 2\left(x^2+y^2\right)=4\left(a^2+b^2\right)\end{array}$$