Not sure how we get from the left to right right hand side of this equation. The idea being that $\displaystyle a_nb_n - lm$ is being expressed in terms of $\displaystyle a_n - l $ and $\displaystyle b_n - m$

$\displaystyle a_nb_n - lm = (a_n - l)(b_n - m) +m(a_n - l) +l(b_n - m)$

Thanks.