`a) x^2 - 3x + xy - 3y`
`= (x^2 - 3x) + (xy - 3y)`
`= x(x - 3) + y(x - 3)`
`= (x + y)(x - 3)`
`b) x^2 - 2x - 4y^2 - 4y`
`= (x^2 - 4y^2) - (2x + 4y)`
`= [x^2 - (2y)^2)] - 2(x + 2y)`
`= (x - 2y)(x + 2y) - 2(x + 2y)`
`= (x + 2y)(x - 2y - 2)`
`c) x^3 + 2x^2 + 2x + 1`
`= x^3 + 2x^2. 1 + 2x. 1^2 + 1^3`
`= (x + 1)^3`
`d) x^4 - 2x^3 + 2x - 1`
`= (x^4 - 1) - (2x^3 - 2x)`
`= [(x^2)^2 - 1^2] - 2x(x^2 - 1)`
`= (x^2 - 1)(x^2 + 1) - 2x(x^2 - 1)`
`= (x^2 - 1)(x^2 + 1 - 2x)`
`e) x^6 - x^4 + 2x^3 + 2x^2`
`= (x^6 - x^4) + (2x^3 + 2x^2)`
`= x^4(x^2 - 1) + 2x^2(x + 1)`
`= x^4(x^2 - 1^2) + 2x^2(x + 1)`
`= x^4(x - 1)(x + 1) - 2x^2(x + 1)`
`= (x + 1)[x^4(x - 1) - 2x^2]`
`= (x + 1)(x^5 - x^4 - 2x^2)`
`f) x^2y + xy^2 + x^2z + y^2z + 2xyz`
`= x^2y + xy^2 + x^2z + xyz + y^2z + xyz`
`= (x^2y + xy^2) + (x^2z + xyz) + (y^2z + xyz)`
`= xy(x + y) + xz(x + y) + yz(y + x)`
`= (x + y)(xy + xz + yz)`
