Question
Factorise the following expressions.
$a^2b + a^2c + ab + ac + b^2c + c^2b$
$a^2b + a^2c + ab + ac + b^2c + c^2b$
✓
Answer
$ a^2 b+a^2 c+a b+a c+b^2 c+c^2 b $
$ \left(a^2 b+a b+b^2 c\right)+\left(a^2 c+a c+c^2 b\right) $
$ =b\left(a^2+a+b c\right)+c\left(a^2+a+b c\right)$
$ =\left(a^2+a+b c\right)(b+c) $
$ \left(a^2 b+a b+b^2 c\right)+\left(a^2 c+a c+c^2 b\right) $
$ =b\left(a^2+a+b c\right)+c\left(a^2+a+b c\right)$
$ =\left(a^2+a+b c\right)(b+c) $
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