`a)`

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

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

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

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

`b)`

`x^3-3x^2+3x-y^3-1`

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

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

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

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

`c)`

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

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

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

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

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

`d)`

`5x^2+5y^2-x^2z+2xyz-y^2z-10xy`

`=(5x^2-10xy+5y^2)-z(x^2-2xy+y^2)`

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

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

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