a) $3x^2 + 5x^3 + x^2y$
$= x^2(3 + 5x + y)$
b) $x^3 +\dfrac{1}{27}$
$=x^3 +\left(\dfrac13\right)^3$
$=\left(x +\dfrac13\right)\left(x^2 -\dfrac13x +\dfrac19\right)$
c) $x^2 - 3x + xy - 3y$
$= x(x-3) + y(x-3)$
$= (x-3)(x+y)$
d) $5x^3 + 10x^2y + 5xy^2$
$= 5x(x^2 + 2xy + y^2)$
$= 5x(x+y)^2$
e) $-3x^2 + 5x^3 - x^2y$
$= x^2(-3 + 5x - y)$
f) $x^3 -\dfrac{1}{27}$
$=x^3 -\left(\dfrac13\right)^3$
$=\left(x -\dfrac13\right)\left(x^2 +\dfrac13x +\dfrac19\right)$
g) $x^2 + 3x + xy + 3y$
$= x(x+3) + y(x+3)$
$= (x+3)(x+y)$
h) $5x^3 - 10x^2y + 5xy^2$
$= 5x(x^2 - 2xy + y^2)$
$= 5x(x-y)^2$
