Question

factorise the above question

Answer 1

Hello there!
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You can factorise the given equation this way:

$= (1 - {x}^{2} )(1 - {y}^{2} ) + 4xy \\ = 1 - {x}^{2} - {y}^{2} + {x}^{2} {y}^{2} + 4xy \\ = (1 + 2xy + {x}^{2} {y}^{2} ) - ( {x}^{2} - 2xy + {y}^{2} ) \\ = {(1 + xy)}^{2} - {(x - y)}^{2} \\ = (1 + xy + (x - y))(1 + xy - (x - y)) \\ = (1 + xy + x - y)(1 + xy - x + y)$
Hence we have factorised the equation!
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Hope this helps!