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`a)`

`2x^3+5x^2-4x`

`=x(2x^2 + 5x-4)`

`b)`

`3x^2y-9xy^2+13x^2y^2`

`=xy (3x -9y+13xy)`

`c)`

`2xy(x-3y)-x(3y-x)`

`=2xy(x-3y)+x(x-3y)`

`=(2xy+x)(x-3y)`

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

`d)`

`2x^2(x+1)^2 +4y^2(1+x)`

`=2x^2(1+x)^2+4y^2(1+x)`

`= (2+2x)[x^2(1+x)+2y^2]`

`= 2(1+x)[x^2(1+x)+2y^2]`

`e)`

`3(x-y)^2+9y(y-x)^2`

`= 3(x-y)^2+9y(x-y)^2`

`= (3+9y)(x-y)^2`

`=3(1+3y)(x-y)^2`

`f)`

`4x^2-12x+9`

`=4x^2 - 6x-6x+9`

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

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

`=(2x-3)^2`