Factorize the equation $a (a - 1) - b (b - 1)$

(a + b) (b - 1)

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(a - b) (a + b - 1)

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(a + b) (a - 1)

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(a - b) (a b)

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Solution

The correct option is A $(a - b) (a + b - 1)$
$a (a - 1) - b (b - 1)$
$= a^{2} - a - b^{2} + b$
$= a^{2} - b^{2} - a + b$
$= (a + b) (a - b) - (a - b)$
$= (a - b) (a + b - 1)$

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