Factorise:
$x^{2} + 3 x - (a^{2} + a - 2)$ .

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Solution

Now,
$x^{2} + 3 x - (a^{2} + a - 2)$
$= x^{2} + 3 x - (a + 2) (a - 1)$
$= x^{2} + {(a + 2) - (a - 1)} x - (a + 2) (a - 1)$
$= x (x + a + 2) - (a - 1) (x + a + 2)$
$= (x + a + 2) (x - a + 1)$ .

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