Factorise : 1 35 +12 35 a+a^2 - Vidyadip

Question

Factorise : $\frac{1}{35}+\frac{12}{35} a+a^2$

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Answer

$\frac{1}{35}+\frac{12}{35} a+a^2 $
$=\frac{1}{35}+\left(\frac{1}{5}+\frac{1}{7}\right) a+a^2$
$ =\frac{1}{35}+\frac{1}{5} a+\frac{1}{7} a+a^2$
$=\frac{1}{5}\left(\frac{1}{7}+a\right)+a\left(\frac{1}{7}+a\right) $
$ =\left(\frac{1}{7}+a\right)\left(\frac{1}{5}+a\right)$

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