Mathematics
Factorise the following:
a(a - 1) - b(b - 1)
Factorisation
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Answer
a(a - 1) - b(b - 1) = a2 - a - b2 + b
= a2 - b2 - a + b
= a2 - b2 - (a - b).
Using identity,
a2 - b2 = (a - b)(a + b).
a2 - b2 - (a - b) = (a - b)(a + b) - (a - b)
= (a - b)(a + b - 1).
Hence, a(a - 1) - b(b - 1) = (a - b)(a + b - 1).
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