How are these different?

where

and

For instance,

My book proves the distributive property of multiplication as follows (im going to leave stuff out)

Then you expand AB+AC and do some regrouping to find A(B+C)=AB+AC

But, in another text I found the same proof done with the afore mentioned notation

I don't understand how to read the latter proof. What's being done in the proof makes sense to me, but I'm just not sure how to read the notation I guess.