`a,x^2-2x-3=x^2-3x+x-3`
`=x(x-3)+(x-3)=(x+1)(x-3)`
`b,x^2+x-y^2+y=(x+y)+(x^2-y^2)`
`=(x+y)(x-y)+(x-y)=(x+y)(x-y+1)`
`c,3x^2+3y^2-6xy-12`
`=3(x^2+y^2-2xy-4)`
`=3[(x-y)^2-4]=3(x-y+2)(x-y-2)`
`d,3x+3y-x^2-2xy-y^2`
`=3(x+y)-(x+y)^2=(3-x-y)(x+y)`
`e,x^3-x+3x^2y+3xy^2-y+y^3`
`=(x+y)^3-(x+y)=(x+y)[(x+y)^2-1]`
`=(x+y)(x+y-1)(x+y+1)`
`f,x^2-y^2+6x+6y`
`=(x-y)(x+y)+6(x+y)`
`=(x-y+6)(x+y)`
`g,y^3-4y^2+3y`
`=y(y^2-4y+3)=y(y^2-3y-y+3)`
`=y[y(y-3)-(y-3)]=y(y-3)(y-1)`