1. The problem is to expand the expression $ (a+b)^2 $. 2. The formula for the square of a binomial is: $$ (x+y)^2 = x^2 + 2xy + y^2 $$ 3. Applying this formula to $ (a+b)^2 $, we get: $$ (a+b)^2 = a^2 + 2ab + b^2 $$ 4. This means when you square the sum of two terms, you square each term and add twice their product. 5. So the expanded form of $ (a+b)^2 $ is: $$ a^2 + 2ab + b^2 $$ This is the final answer.