`a) x^2 - 2x - 4y^2 - 4y`

`= ( x - 2y )( x + 2y ) - 2( x + 2y )`

`= ( x + 2y )( x - 2y -2 )`

`b) x^4 + 2x^3 - 4x - 4`

`= x^4 + 2x^3 + x^2 - x^2 - 4x - 4 `

`= ( x^2 + x )^2 -( x + 2 )^2`

`= ( x^2 + x - x - 2 )( x^2 + x + x + 2 )`

`= ( x^2 - 2 )( x^2 + 2x + 2 )`

`c) x^2( 1 - x^2 ) - 4 - 4x^2`

`= x^2 - x^4 - 4x^2 - 4`

`= x^2 - ( x^2 + 2 )^2`

`= ( x - x^2 - 2 )( x + x^2 + 2 )`

`d) ( 1 + 2x )( 1 - 2x ) - x( x + 2 )( x - 2 )`

`= 1 - 4x^2 - x( x^2 - 4 )`

`= 1 - 4x^2 - x^3 + 4x`

`= ( 1 - x )( 1 + x + x^2 ) + 4x( 1 - x )`

`= ( 1 - x )( x^2 + 5x + 1 )`

`e) x^2 + y^2 - x^2y^2 + xy - x - y`

`= x^2( 1 - y^2 ) + y( y - 1 ) + x( y - 1 )`

`= -x^2( y - 1 )( y + 1 ) + y( y - 1 ) + x( x - 1 )`

`= ( y- 1 )( -x^2y - x^2 + x + y )`