Question

Factorise:
6ab − b² + 12ac − 2bc

Answer 1

By suitably arranging the terms:
$$\begin{gathered} 6ab-b^2+12ac-2bc=6ab+12ac-b^2-2bc \\ =\left(6ab+12ac\right)-\left(b^2+2bc\right) \\ =6a\left(b+2c\right)-b\left(b+2c\right) \\ =\left(b+2c\right)\left(6a-b\right) \end{gathered}$$

∴ $6ab-b^2+12ac-2bc=\left(b+2c\right)\left(6a-b\right)$