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Mathematics

Factorise :

3 - 5x + 5y - 12(x - y)2

Factorisation

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Answer

Given,

    3 - 5x + 5y - 12(x - y)2

= 3 - 5(x - y) - 12(x - y)2

Substituting x - y = a, we get :

= 3 - 5a - 12a2

= 3 - 9a + 4a - 12a2

= 3(1 - 3a) + 4a(1 - 3a)

= (1 - 3a)(3 + 4a)

= [1 - 3(x - y)][3 + 4(x - y)]

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

Hence, 3 - 5x + 5y - 12(x - y)2 = (1 - 3x + 3y)(3 + 4x - 4y).

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