`a) 4x^2(x - 3y) - 8x(x - 3y)`

`= (4x^2 - 8x)(x - 3y)`

`= 4x(x - 2)(x - 3y)`

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

`= (x^2 + 2x) - (2xy + 4y)`

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

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

`c) x^3 + 2x^2y - 4xy^2 - 8y^3`

`= (x^3 - 8y^3) + (2x^2y - 4xy^2)`

`= (x - 2y)(x^2 + 2x + 4y^2) + 2xy(x - 2y)`

`= (x^2 + 2xy + 4y^2 + 2xy)(x - 2y)`

`= (x^2 + 4xy + 4y^2)(x-2y)`

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

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