PDF chapter test

Factorisation by grouping the terms and then taking terms commonly outside
The terms of a given expression are need to be grouped suitably in such a way that they have a common factor so that the factorisation is easy to take out common factor
from those terms.

Consider the expression $3{m}^{2}+\mathit{mn}+3\mathit{mn}+{n}^{2}$.

Let us take the common factor for the first two terms separately and take the common factor second two terms separately.

$\underset{¯}{3{m}^{2}+\mathit{mn}}+\underset{¯}{3\mathit{mn}+{n}^{2}}$

$=m\left(3m+n\right)+n\left(3m+n\right)$

$=\left(3m+n\right)\left(m+n\right)$