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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.

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.

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

$=m(3m+n)+n(3m+n)$

$=(3m+n)(m+n)$