Question

Factorise:
9a² + 6a + 1 – 36b²

Answer 1

$$\begin{gathered} 9a^2+6a+1-36b^2 \\ =\left[{\left(3a\right)}^2+2\times 3a\times 1+1^2\right]-{\left(6b\right)}^2 \\ ={\left(3a+1\right)}^2-{\left(6b\right)}^2\left[a^2+2ab+b^2={\left(a+b\right)}^2\right] \\ =\left(3a+1-6b\right)\left(3a+1+6b\right)\left[a^2-b^2=\left(a-b\right)\left(a+b\right)\right] \\ =\left(3a-6b+1\right)\left(3a+6b+1\right) \end{gathered}$$