`a) 2xy(x - y) - xy + y^2`

`= 2xy(x - y) - (xy - y^2)`

`= 2xy(x - y) - y(x - y)`

`= (x - y)(2xy - y)`

`= y(x - y)(2x - 1)`

`b) x^2 - 4y^2 - x - 2y`

`= (x^2 - (2y)^2) - (x + 2y)`

`= (x - 2y)(x + 2y) - (x + 2y)`

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

`c) (x - 2)^3 - x + 2`

`= (x - 2)^3 - (x - 2)`

`= (x - 2)[(x - 2)^2 - 1]`

`= (x - 2)(x - 2 - 1)(x - 2 + 1)`

`= (x - 2)(x - 3)(x - 1)`

`d) 3xy - 4y - 3x + 4`

`= (3xy - 4y) - (3x - 4)`

`= y(3x - 4) - (3x - 4)`

`= (3x - 4)(y - 1)`

`e) x^2 - 4xy + 3y^2`

`= x^2 - xy - 3xy + 3y^2`

`= x(x - y) - 3y(x - y)`

`= (x - y)(x - 3y)`

`f) x^2 - y^2 + 5x - 5y`

`= (x^2 - y^2) + (5x - 5y)`

`= (x - y)(x + y) + 5(x - y)`

`= (x - y)(x + y + 5)`

`g) x^2 - x + 1/4`

`= x^2 - 2*x*1/2 + (1/2)^2`

`= (x - 1/2)^2`

`h) x^3 - 6x^2 + 12x - 8`

`= x^3 - 3*x^2*2 + 3*x*2^2 - 2^3`

`= (x - 2)^3`