`a,x-2y+x^2-4y^2`
`=(x-2y)+(x-2y)(x+2y)`
`=(x-2y)(x+2y+1)`
`b,x^2-4x^2y^2+y^2+2xy`
`=(x^2+2xy+y^2)-4x^2y^2`
`=(x+y)^2-(2xy)^2`
`=(x+y-2xy)(x+y+2xy)`
`c,x^6-x^4+2x^3+2x^2`
`=x^4(x^2-1)+2x^2(x+1)`
`=x^4(x-1)(x+1)+2x^2(x+1)`
`=(x+1)(x^5-x^4+2x^2)`
`=x^2(x+1)(x^3-x^2+2)`
`=x^2(x+1)(x^3+x^2-2x^2+2)`
`=x^2(x+1)[x^2(x+1)-2(x-1)(x+1)]`
`=x^2(x+1)(x+1)(x^2-2x+1)`
`=x^2(x+1)^2(x-1)^2`
`d,x^3+3x^2+3x+1-8y^3`
`=(x+1)^3-(2y)^3`
`=(x+1-2y)[(x+1)^2+2y(x+1)+4y^2]`
`=(x-2y+1)(x^2+2x+1+2xy+2+4y^2)`
`=(x-2y+1)(x^2+2x+2xy+4y^2+2)`
