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Factorise x^2-y^2-2x+6y-8

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x^2 - y^2 - 2x + 6y - 8
= (x^2 - 2x + 1) - (y^2 - 6y + 9) - 8 - 1 + 9
= (x - 1)^2 - (y - 3)^2
= [(x - 1) - (y - 3) ] [(x - 1) + (y - 3)]
= (x - 1 - y + 3) ( x - 1 + y - 3)
= (x - y + 2) (x + y - 4)
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