Question

Factorize:
8a² − 27ab + 9b²

Answer 1

We have:
$8a^2-27ab+9b^2$

We have to split ($-$27) into two numbers such that their sum is ($-$27) and their product is 72, i.e., $8\times 9$.
Clearly, $\left(-24\right)+\left(-3\right)=-27\mathrm{and}\left(-24\right)\times \left(-3\right)=72$.

$$\begin{gathered} \therefore 8a^2-27ab+9b^2=8a^2-24ab-3ab+9b^2 \\ =8a(a-3b)-3b(a-3b) \\ =(a-3b)(8a-3b) \end{gathered}$$