I am having a problem multiplying these fractions:

$\displaystyle \frac{x^2y^2}{m^3n} * \frac{5a+5b}{2d^2+2d} =$

This is the process I know for solving these:

1. Factor the numerators and denominators of both fractions.

2. Cross out the common factors. Now I can see what the answer is.

But that isn't working here. I can't find any common factors, so I can't get rid of them:

$\displaystyle \frac{x*x*y*y}{m*m*m*n}* \frac{5(a+b)}{2d(d+1)} =$

The answer is $\displaystyle \frac{y^2}{m^2nx}$ but knowing the answer is useless to me because I don't know how to get there.

What am I doing wrong? Is there a different way to multiply fractions? Am I factoring wrong? Why does an x end up in the denominator?