Mathematics
Factorise the following:
x - 2y - x2 + 4y2
Factorisation
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Answer
x - 2y - x2 + 4y2
= x - 2y - (x2 - 4y2)
= x - 2y - [x2 - (2y)2].
Using identity,
a2 - b2 = (a - b)(a + b).
(x - 2y) - [x2 - (2y)2] = (x - 2y) - (x - 2y)(x + 2y)
= (x - 2y)[1 - (x + 2y)]
= (x - 2y)(1 - x - 2y).
Hence, x - 2y - x2 + 4y2 = (x - 2y)(1 - x - 2y).
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