Đáp án:

a)
$(x+y)^2 - 2(x+y)z + z^2 = ((x+y) - z)^2 = (x+y-z)^2$.

b) $x+y - 5x^2+5y^2$
$= (x+y) - 5(x^2 - y^2)$
$= (x+y) - 5(x-y)(x+y)$
$= (x+y) [1 - 5(x-y)]$
$= (x+y) (1 - 5x + 5y)$

c) $x^3 + 3x^2y - 4xy^2 - 12y^3$
$= x^2(x+3y) - 4y^2(x+3y)$
$= (x^2 - 4y^2)(x+3y)$
$= (x-2y)(x+2y)(x+3y)$

d) $x^3 + 4y^2 - 2xy + x^2 + 8y^3$
$= (x^3 + 8y^3) + (x^2 - 2xy + 4y^2)$
$= (x+2y)(x^2 - 2xy + 4y^2) + (x^2 - 2xy + 4y^2)$
$= (x^2 - 2xy + 4y^2)(x+2y+1)$