Step 1

To factorise: \(\displaystyle{21}{m}^{{{2}}}+{13}{m}{n}+{2}{n}^{{{2}}}\)

Solution:

\(\displaystyle{21}{m}^{{{2}}}+{13}{m}{n}+{2}{n}^{{{2}}}\)

On simplifying further, we get:

\(\displaystyle{21}{m}^{{{2}}}+{13}{m}{n}+{2}{n}^{{{2}}}={21}{m}^{{{2}}}+{\left({7}{m}{n}+{6}{m}{n}\right)}+{2}{n}^{{{2}}}\)

\(\displaystyle={\left({21}{m}^{{{2}}}+{7}{m}{n}\right)}+{\left({6}{m}{n}+{2}{n}^{{{2}}}\right)}\)

=7m(3m+n)+2n(3m+n)

=(3m+n)(7m+2n)

\(\displaystyle\Rightarrow{21}{m}^{{{2}}}+{13}{m}{n}+{2}{n}^{{{2}}}={\left({3}{m}+{n}\right)}{\left({7}{m}+{2}{n}\right)}\)

Step 2

Result:

\(\displaystyle{21}{m}^{{{2}}}+{13}{m}{n}+{2}{n}^{{{2}}}={\left({3}{m}+{n}\right)}{\left({7}{m}+{2}{n}\right)}\)

To factorise: \(\displaystyle{21}{m}^{{{2}}}+{13}{m}{n}+{2}{n}^{{{2}}}\)

Solution:

\(\displaystyle{21}{m}^{{{2}}}+{13}{m}{n}+{2}{n}^{{{2}}}\)

On simplifying further, we get:

\(\displaystyle{21}{m}^{{{2}}}+{13}{m}{n}+{2}{n}^{{{2}}}={21}{m}^{{{2}}}+{\left({7}{m}{n}+{6}{m}{n}\right)}+{2}{n}^{{{2}}}\)

\(\displaystyle={\left({21}{m}^{{{2}}}+{7}{m}{n}\right)}+{\left({6}{m}{n}+{2}{n}^{{{2}}}\right)}\)

=7m(3m+n)+2n(3m+n)

=(3m+n)(7m+2n)

\(\displaystyle\Rightarrow{21}{m}^{{{2}}}+{13}{m}{n}+{2}{n}^{{{2}}}={\left({3}{m}+{n}\right)}{\left({7}{m}+{2}{n}\right)}\)

Step 2

Result:

\(\displaystyle{21}{m}^{{{2}}}+{13}{m}{n}+{2}{n}^{{{2}}}={\left({3}{m}+{n}\right)}{\left({7}{m}+{2}{n}\right)}\)