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Mathematics

Factorise the following:

4(2a - 3)2 - 3(2a - 3)(a - 1) - 7(a - 1)2

Factorisation

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Answer

Let (2a - 3) = x and (a - 1) = y,

∴ 4(2a - 3)2 - 3(2a - 3)(a - 1) - 7(a - 1)2 = 4x2 - 3xy - 7y2.

Factorising we get,

4x2 - 3xy - 7y2 = 4x2 - 7xy + 4xy - 7y2

= x(4x - 7y) + y(4x - 7y)

= (x + y)(4x - 7y).

= [(2a - 3) + (a - 1)][4(2a - 3) - 7(a - 1)]

= (3a - 4)(8a - 12 - 7a + 7)

= (3a - 4)(a - 5).

Hence, 4(2a - 3)2 - 3(2a - 3)(a - 1) - 7(a - 1)2 = (3a - 4)(a - 5).

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