Factorise : $a^{3} - a^{2} - a b + a + b - 1$

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Solution

$a^{3} - a^{2} - a b + a + b - 1 = a^{3} - a^{2} - a b + b + a - 1 = a^{2} (a - 1) - b (a - 1) + 1 (a - 1) = (a - 1) (a^{2} - b + 1)$

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