Mathematics
Factorise the following:
4(a - 1)2 - 4(a - 1) - 3
Factorisation
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Answer
Let (a - 1) = t.
4(a - 1)2 - 4(a - 1) - 3 = 4t2 - 4t - 3.
Factorising we get,
4t2 - 4t - 3 = 4t2 - 6t + 2t - 3.
= 2t(2t - 3) + 1(2t - 3)
= (2t - 3)(2t + 1)
= [2(a - 1) - 3][2(a - 1) + 1]
= [2a - 2 - 3][2a - 2 + 1]
= (2a - 5)(2a - 1).
Hence, 4(a - 1)2 - 4(a - 1) - 3 = (2a - 5)(2a - 1).
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