QM- Proving the uncertainty relation - Commutators

Folks,

I am stuck on the derivation of the uncertainty relation when using the commutator and anti commutator...

given

Above on the RHS is the commutator and anti-commutator respectively. I dont understand the next line for the commutator

the last term in the above line is 0 because <A> is a c number

where the last term in the above line is also 0 for same reason.

Now I do know [A,B] is AB-BA but I dont know where this algebaic derivation is coming out of..

Thanks