Question: Expand the square: $$(x+2)^2 = x^2 + 2 \cdot x \cdot 2 + 2^2 = x^2 + 4x + 4$$
1. **State the problem:** Expand the square of the binomial $$(x+2)^2$$.
2. **Formula used:** The expansion of a binomial square is given by the formula:
$$ (a+b)^2 = a^2 + 2ab + b^2 $$
where $a = x$ and $b = 2$ in this case.
3. **Apply the formula:**
$$ (x+2)^2 = x^2 + 2 \cdot x \cdot 2 + 2^2 $$
4. **Calculate each term:**
- $x^2$ remains as is.
- $2 \cdot x \cdot 2 = 4x$
- $2^2 = 4$
5. **Write the expanded form:**
$$ x^2 + 4x + 4 $$
6. **Explanation:**
When you square a binomial, you square each term and add twice the product of the two terms. This is why the middle term is $4x$, which is twice the product of $x$ and $2$.
**Final answer:**
$$ (x+2)^2 = x^2 + 4x + 4 $$