In 1/2 A + 1/2 B = 1/2(A+B), you are not distributing anything. You are factoring out the 1/2.
In the reverse 1/2(A+B)=1/2 A + 1/2 B, you are distributing out the 1/2 and removing parentheses.
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In 1/2 A + 1/2 B = 1/2(A+B), you are not distributing anything. You are factoring out the 1/2.
In the reverse 1/2(A+B)=1/2 A + 1/2 B, you are distributing out the 1/2 and removing parentheses.