Factorise the following: 4(a - 1) 2 - 4(a - 1) - 3

Let (a - 1) = t. 4(a - 1) 2 - 4(a - 1) - 3 = 4t 2 - 4t - 3. Factorising we get, 4t 2 - 4t - 3 = 4t 2 - 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).

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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Factorise the following:4(a - 1)2 - 4(a - 1) - 3

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