simplify (1/2A + 1/2B) ^2

Notice that both A and B are multiplied by (1/2).

Thus, the given expression can be re-written as [ (1/2) (A+B) ]^2.

Square the (1/2) and the (A+B) separately, and then multiply together the resulting squares:

(1/4) (A^2 + 2AB + B^2)

A^2 ab b^2

___ + ___ + ___

4 2 4

this is your answer