Question

Which of the following is the correct factorisation of a(a-1)-b(b-1)

Answer 1

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

writing above in expanded form

= a²-a-b²+b

rearranging above

= a²-b²-(a-b)

expanding a²-b²

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

taking (a-b) as common factor

(a-b)[(a+b)-1]

simplifying square bracket

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

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