Select the expressions that are equivalent to $$ 4(4 a+1)+2 $$. $$ \begin{array}{l}16 a+6 \ 6 a+16 \ (4 a+1) 4+2 \ 4(2 a+2 a+1)+2\end{array} $$

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To determine which expressions are equivalent to $$ 4(4a + 1) + 2 $$, let's simplify and compare each option.

1. **$$ 16a + 6 $$**
   $$
   4(4a + 1) + 2 = 16a + 4 + 2 = 16a + 6
   $$
   This **is equivalent**.

2. **$$ 6a + 16 $$**
   $$
   6a + 16 \neq 16a + 6 \quad \text{(unless $$ a = 1 $$, which isn't generally true)}
   $$
   This **is not equivalent**.

3. **$$ (4a + 1) \cdot 4 + 2 $$**
   $$
   (4a + 1) \cdot 4 + 2 = 4(4a + 1) + 2
   $$
   This is the **same as the original expression**, so it **is equivalent**.

4. **$$ 4(2a + 2a + 1) + 2 $$**
   $$
   4(2a + 2a + 1) + 2 = 4(4a + 1) + 2
   $$
   This simplifies to the **original expression**, so it **is equivalent**.

**Therefore, the equivalent expressions are:**

- $$ 16a + 6 $$
- $$ (4a + 1) \cdot 4 + 2 $$
- $$ 4(2a + 2a + 1) + 2 $$

**Answer:** All except the second expression are equivalent to $$4(4a+1)+2$$.
The equivalent expressions are $$16a + 6$$, $$(4a + 1) \cdot 4 + 2$$, and $$4(2a + 2a + 1) + 2$$.

Select the expressions that are equivalent to .

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