Factor the binomial $36 m^2 - \frac{25}{4} $ OK, I got a new one... it's $36 m^2 - \frac{25}4 $
and I got:
$(18m-\frac{5}2 )(18m+\frac{5}2 )$ although that is incorrect... where did I go wrong? 

I don't think you are right,since:
$$ 36 m^2 - \frac{25}4 = (6m)^2 - \left(\frac{5}2 \right)^2 = \left(6m + \frac{5}2 \right)\left(6m - \frac{5}2 \right) $$ 
