Question 88 (xvii)

Factorise the following expression.

$a^{2} b + a^{2} c + a b + a c + b^{2} c + c^{2} b$

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Solution

We have, $a^{2} b + a^{2} c + a b + a c + b^{2} c + c^{2} b$
$= (a^{2} b + a b + b^{2} c) + (a^{2} c + a c + c^{2} b)$
$= b (a^{2} + a + b c) + c (a^{2} + a + b c)$
$= (a^{2} + a + b c) (b + c)$

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