`1,`

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

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

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

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

`2,`

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

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

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

`3,`

`2x(x-2)-(x-2)^2`

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

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

`4,`

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

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

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

`= (1-x)^2(4x-1)`

`5,`

`3x(x+2)-5(x+2)^2`

`= (x+2).[3x-5(x+2)]`

`= (x+2)(3x-5x+10)`

`= (x+2)(-2x+10)`

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

`6,`

`4x(x-y)+3(y-x)^2`

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

`= (x-y).[4x+3(x-y)]`

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

`= (x-y)(7x-3y)`

`#TD`