When asked to convert something like $\frac{1}{(ax+b)(cx+d)}$ to partial fractions, I can say
$\frac{1}{(ax+b)(cx+d)} = \frac{A}{ax+b} + \frac{B}{cx+d}$
Then why can't I split $(cx+d)^2$ into $(cx+d)(cx+d)$ then do
$\frac{1}{(ax+b)(cx+d)^2} = \frac{A}{ax+b} + \frac{B}{cx+d} + \frac{C}{cx+d}$
The correct way is
$\frac{1}{(ax+b)(cx+d)^2} = \frac{A}{ax+b} + \frac{B}{cx+d} + \frac{C}{(cx+d)^2}$