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Mathematics

Factorise :

4(2x - 3y)2 - 8x + 12y - 3

Factorisation

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Answer

Given,

    4(2x - 3y)2 - 8x + 12y - 3

= 4(2x - 3y)2 - 4(2x - 3y) - 3

Substituting (2x - 3y) = a, we get :

= 4a2 - 4a - 3

= 4a2 - 6a + 2a - 3

= 2a(2a - 3) + 1(2a - 3)

= (2a + 1)(2a - 3)

= [2(2x - 3y) + 1][2(2x - 3y) - 3]

= (4x - 6y + 1)(4x - 6y - 3).

Hence, 4(2x - 3y)2 - 8x + 12y - 3 = (4x - 6y + 1)(4x - 6y - 3).

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