1. Stating the problem: Simplify the expression $(x+2)^2$. 2. Use the formula for the square of a binomial: $$(a+b)^2 = a^2 + 2ab + b^2$$. 3. In this case, $a = x$ and $b = 2$, so substitute: $$ (x+2)^2 = x^2 + 2 \cdot x \cdot 2 + 2^2 $$ 4. Calculate each term: $$ x^2 + 4x + 4 $$ 5. Final simplified expression: $$ x^2 + 4x + 4 $$ This is the expanded form of $(x+2)^2$.