The factors of (a2 + 4b2 + 4b - 4ab - 2a - 8) are?

Answer: Option A

$$\begin{array}{rl}& a^2+4b^2+4b-4ab-2a-8\\ & =a^2-4ab+4b^2-2a+4b-8\\ & ={\left(a-2b\right)}^2-2\left(a-2b\right)-8\\ & \text{Put }t=a-2b\\ & =t^2-2t-8\\ & =t^2-4t+2t-8\\ & =t\left(t-4\right)+2\left(t-4\right)\\ & =\left(t+2\right)\left(t-4\right)\\ & =\left(a-2b-4\right)\left(a-2b+2\right)\\ & \left(\text{Put the value of assume }t\right)\end{array}$$