Factorise $(a - 1) - (a - 1)^{2} + a b - b$ .

$(a - 1) (2 - a)$

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$(a - 1) (2 - a + b)$

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

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

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Solution

The correct option is B
$(a - 1) (2 - a + b)$

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

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

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