Factorise:

$a^{3} + 2 a^{2} - a - 2$

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Solution

$a^{3} + 2 a^{2} - a - 2$

= $a^{2} (a + 2) - 1 (a + 2)$

= $(a + 2) (a^{2} - 1)$

= $(a + 2) (a + 1) (a - 1)$

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