a) 4`x^2`-4xy+`y^2`
= `(2x)^2`-4xy+`y^2`
= `(2x-y)^2`
= (2x-y)(2x-y)
b) `(x+1)^2`-9`y^2`
= `(x+1)^2`-`(3y)^2`
= (x+1+3y)(x+1-3y)
c) $x^{4}$ $y^{4}$ + 4$x^{2}$ $y^{2}$ +4
= $($x^{2}$ $y^{2}$)^{2}$+4$x^{2}$ $y^{2}$+`2^2`
= $($x^{2}$ $y^{2}$+2)^{2}$
= ($x^{2}$ $y^{2}$+2)($x^{2}$ $y^{2}$+2)
d) `y^2`-4y+4-`x^2`
= (`y^2`-4y+4)-`x^2`
= `(y-2)^2`-`x^2`
= (y-2+x)(y-2-x)