a, `x^3-1+5x^2-5+3x-3`
`=(x-1)(x^2+x+1)+5(x^2-1)+3(x-1)`
`=(x-1)(x^2+x+1)+(5x+5)(x-1)+3(x-1)`
`=(x-1)(x^2+x+1+5x+5+3)`
`=(x-1)(x^2+6x+9)`
`=(x-1)(x+3)^2`
b, `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)`
`=(x+y-1)(x^2+y^2-xy-2x-y+1)`
c, `x^3-x^2-x+1`
`=x^2(x-1)-(x-1)`
`=(x-1)(x^2-1)`
`=(x-1)^2(x+1)`
d, `5x^3-3x^2y-45xy^2 +27y^3`
`=(5x^3-45xy^2) - (3x^2y-27y^3)`
`=5x(x^2-9y^2) - 3y(x^2-9y^2)`
`=(x^2-9y^2)(5x-3y)`
`=(x-3y)(x+3y)(5x-3y)`
e, `x^4-x^2+2x-1`
`=x^4-(x^2-2x+1)`
`=x^4-(x-1)^2`
`=(x^2+x-1)(x^2-x+1)`
f, `4a^2b^2 - (a^2+b^2-1)^2`
`=(a^2+b^2-1+2ab)(-a^2-b^2+1+2ab)`
`=((a+b)^2-1)(1-(a-b)^2)`
`=(a+b+1)(a+b-1)(a-b+1)(-a+b+1)`
