\begin{array}{c}\color{#003366}{-Re}\color{#005A9C}{dD}\color{#007ACC}{e}\color{#00AEEF}{vi}\color{#00CFFF}{ls}\color{#A4D3EE}{-}\color{#D3D3D3}{}\color{#E0E0E0}{}\end{array}

`a)`

`x^2-2x+2y-y^2`

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

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

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

`b)`

`3x^3+xy-12xy^2-2y^2`

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

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

`=(x-2y)[3x(x+2y)+y]`

`=(x-2y)(3x^2+6xy+y)`

`c)`

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

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

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

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

`d)`

`16x^4-8x^2-y^2+1`

`=(16x^4-8x^2+1)-y^2`

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

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