My question is regarding Bohr's equation, which, from what I understand (please correct me if I'm wrong), is used to calculate the energy gained or lost when an electron changes "states" (n=1, n=2, etc). Not exactly sure what a "state" is...although I know that a change in "state" from higher to lower results in the emission of a photon. Are "states" the same as orbitals?
Anyway, my main question is how this equation went from step 1 to step 3:
/\E= Efinal - Einitial
= (-2.18 x 10-18 J)(1/nf2) - (-2.18 x 10-18 J)(1/ni2)
= -2.18 x 10-18 J (1/nf2 - 1/nf2)
I know this has something to do with factoring -- but I forgot the rules that govern factoring. Like -2x-(-3x)=?
I should know this but it's been several years since my last math class.