`a)x^3 - 4x^2 + 12x -27 `
`=x^3 - 3x^2 - x^2 + 3x + 9x -27`
`=x^2(x-3) - x(x-3) + 9(x-3)`
`=(x-3)(x^2 - x + 9)`
`c)x^2 - 2x - 4y^2 - 4y`
`=x² - 2x + 1 - 4y^2 - 4y - 1`
`=(x - 2x + 1) - (4y^2 + 4y + 1)`
` =(x-1)^2 - (2y + 1)^2`
`=[(x-1) - (2y+1)][(x-1) + (2y + 1)]`
`=(x - 1 - 2y -1)(x -1 + 2y +1)`
`=(x -2y -2)(x +2y)`
e`)x^2 + y^2 - x^2y^2 + xy - x -y`
`=x^2 - x^2y^2 - x -y + y^2 + xy`
=`x^2(1-y^2) -(x+y) +y(y+x)`
`=x^2(1-y)(1+y) -(x+y)(1 - y)`
`=(1-y)[x^2(1+y) - (x+y)]`
`=(1-y)(x^2 + x^2y - x - y)`
