Question: User: $(4x+2)(2x+1)$
1. **State the problem:** Simplify the expression $$(4x+2)(2x+1)$$.
2. **Formula used:** To multiply two binomials, use the distributive property (also known as FOIL method for binomials):
$$ (a+b)(c+d) = ac + ad + bc + bd $$
3. **Apply the formula:**
$$ (4x+2)(2x+1) = 4x \cdot 2x + 4x \cdot 1 + 2 \cdot 2x + 2 \cdot 1 $$
4. **Calculate each term:**
$$ 4x \cdot 2x = 8x^2 $$
$$ 4x \cdot 1 = 4x $$
$$ 2 \cdot 2x = 4x $$
$$ 2 \cdot 1 = 2 $$
5. **Combine like terms:**
$$ 8x^2 + 4x + 4x + 2 = 8x^2 + \cancel{4x + 4x} + 2 = 8x^2 + 8x + 2 $$
6. **Final answer:**
$$ 8x^2 + 8x + 2 $$