$x^{2}$ - $2x^{}$ - $4y^{2}$ - $4y^{}$
= $x^{2}$ - $2x^{}$ + $1^{}$- $4y^{2}$ - $4y^{}$ - $1^{}$
= ( $x^{2}$ - $2x^{}$ + $1^{}$ ) - ( $4y^{2}$+ $4y^{}$ + $1^{}$ )
= $(x-1)^{2}$ - $(2y+1)^{2}$
= $(x - 1 - 2y - 1 )^{}$$(x - 1 + 2y + 1 )^{}$
= $(x - 2y - 2)^{}$$(x + 2y )^{}$.