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Mathematics

Factorise :

1 - 3x - 3y - 4(x + y)2

Factorisation

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Answer

1 - 3x - 3y - 4(x + y)2

= 1 - 3(x + y) - 4(x + y)2

= 1 - (4 - 1)(x + y) - 4(x + y)2

= 1 - 4(x + y) + 1(x + y) - 4(x + y)2

= (1 - 4(x + y)) + (1(x + y) - 4(x + y)2)

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

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

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

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

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

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