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Question
Factorise: a2−b2−a+b
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Solution
We know the identity a2−b2=(a+b)(a−b)
Using the above identity, the given expression a2−b2−a+b can be factorised as follows:
a2−b2−a+b=[(a+b)(a−b)]−1(a−b)=(a−b)(a+b−1)
Hence, a2−b2−a+b=(a−b)(a+b−1)
We know the identity a2−b2=(a+b)(a−b)
Using the above identity, the given expression a2−b2−a+b can be factorised as follows:
a2−b2−a+b=[(a+b)(a−b)]−1(a−b)=(a−b)(a+b−1)
Hence, a2−b2−a+b=(a−b)(a+b−1)
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