Factorize :
$a^{7} + a b^{6}$

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Solution

$a^{7} + a b^{6}$
$= a (a^{6} + b^{6})$
$= a [(a^{2})^{3} + (b^{2})^{3}]$
$= a (a^{2} + b^{2}) [(a^{2})^{2} - a^{2} b^{2} + (b^{2})^{2}]$
$= a (a^{2} + b^{2}) (a^{4} - a^{2} b^{2} + b^{4})$

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