Question: Expand the square: $ (x+2)^2 = x^2 + 4x + 4 $
1. **State the problem:** We want to expand the square of the binomial $ (x+2)^2 $. This means rewriting it as a sum without parentheses.
2. **Formula used:** The formula for expanding a square of a binomial is:
$$ (a+b)^2 = a^2 + 2ab + b^2 $$
where $a$ and $b$ are any expressions.
3. **Apply the formula:** Here, $a = x$ and $b = 2$.
4. **Calculate each term:**
- $a^2 = x^2$
- $2ab = 2 \times x \times 2 = 4x$
- $b^2 = 2^2 = 4$
5. **Write the expanded form:**
$$ (x+2)^2 = x^2 + 4x + 4 $$
6. **Explanation:** When you square a binomial, you multiply it by itself:
$$ (x+2)(x+2) $$
Using distributive property (FOIL method):
$$ x \times x + x \times 2 + 2 \times x + 2 \times 2 = x^2 + 2x + 2x + 4 $$
Combine like terms:
$$ x^2 + \cancel{2x} + \cancel{2x} + 4 = x^2 + 4x + 4 $$
This is how the expansion works step-by-step.