Factorise $x^{2} - 2 x + 1 - x + 1$ .

$(x - 2) (x - 1)$

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$(x + 2) (x - 1)$

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$(x + 1) (x - 1)$

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$(x - 2) (x + 1)$

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Solution

The correct option is A
$(x - 2) (x - 1)$

We need to factorise the given expression.

$x^{2} - 2 x + 1 - x + 1$

$= (x - 1)^{2} - x + 1$
[Since $(a - b)^{2} = a^{2} - 2 a b + b^{2}$ , we have ( $x - 1)^{2} = x^{2} - 2 x + 1.$ ]

$= (x - 1) (x - 1) - 1 (x - 1)$

$= (x - 1) (x - 1 - 1)$
(Taking $x - 1$ common)

$= (x - 1) (x - 2)$

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