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

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)