Factorize:
$x^{2} + a x - (6 a^{2} - 5 a b + b^{2})$ .

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Solution

Now,
$x^{2} + a x - (6 a^{2} - 5 a b + b^{2})$
$= x^{2} + a x - (6 a^{2} - 3 a b - 2 a b + b^{2})$
$= x^{2} + a x - (3 a - b) (2 a - b)$
$= x^{2} + {(3 a - b) - (2 a - b)} x - (3 a - b) (2 a - b)$
$= x (x + 3 a - b) - (2 a - b) (x + 3 a - b)$
$= (x + 3 a - b) (x - 2 a + b)$

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