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

Solution (By Examveda Team)

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