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Factorise : 1 + 2ab – (a^2 + b^2)

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Factorise : 1 + 2ab – (a2  + b2)

(a) (1 – a + b) (1 – a – b) 

(b) (1 + a + b) (1 – a + b) 

(c) (1 + a – b) (1 – a + b) 

(d) (1 + a – b) (1 + a + b)

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Best answer

(c) (1 + a - b)(a - a + b)

1 + 2ab – (a2 + b2)

= 1 + 2ab - a2 - b2

= 1 - (a2 - 2ab + b2)

= 1 - (a - b)2

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

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