a,
$x^2-x-y^2-y$
$=(x^2-y^2)-(x+y)$
$=(x-y)(x+y)-(x+y)$
$=(x+y)(x-y-1)$
b,
$4x^2-2x-y^2+y$
$=(4x^2-y^2)-(2x-y)$
$=(2x-y)(2x+y)-(2x-y)$
$=(2x-y)(2x+y-1)$
c,
$x^2-3x-9y^2-9y$
$=(x^2-9y^2)-3(x+3y)$
$=(x-3y)(x+3y)-3(x+3y)$
$=(x+3y)(x-3y-3)$
d,
$x^4-x^3-x^2+1$
$=x^3(x-1)-(x+1)(x-1)$
$=(x^3-x-1)(x-1)$
e,
$x^4+x^3+x^2-1$
$=x^3(x+1)+(x-1)(x+1)$
$=(x^3+x-1)(x+1)$
f,
$x^3-y^3-x+y$
$=(x-y)(x^2+xy+y^2)-(x-y)$
$=(x-y)(x^2+xy+y^2-1)$
g,
$125-x^3+5xy-x^2y$
$=(5-x)(25+5x+x^2)+xy(5-x)$
$=(5-x)(25+5x+x^2+xy)$
h,
$x^3-3x^2y-3xy^2+y^3$
$=(x^3+y^3)-3xy(x+y)$
$=(x+y)(x^2-xy+y^2)-3xy(x+y)$
$=(x+y)(x^2-xy+y^2-3xy)$
$=(x+y)(x^2-4xy+y^2)$
