Consider the following expression. $$ \begin{array}{l}2 x+1+5 y \ \text { Select all of the true statements below. } \ \square 5 y \text { and } 1 \text { are like terms. } \ \square 1 \text { is a constant. } \ \square 2 x+1+5 y \text { is written as a product of three factors. } \ \square 5 \text { is a coefficient. } \ \square 2 x+1+5 y \text { is written as a sum of three terms. } \ \square \text { None of these are true. }\end{array} $$

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Let's analyze each statement regarding the expression $$ 2x + 1 + 5y $$:

1. **Statement:** $$ 5y $$ and $$ 1 $$ are like terms.
   - **Analysis:** Like terms are terms that have the same variable raised to the same power. Here, $$ 5y $$ has the variable $$ y $$, while $$ 1 $$ is a constant. Therefore, they are not like terms.
   - **Conclusion:** False.

2. **Statement:** $$ 1 $$ is a constant.
   - **Analysis:** A constant is a term that does not contain any variables. The term $$ 1 $$ does not have any variables and is indeed a constant.
   - **Conclusion:** True.

3. **Statement:** $$ 2x + 1 + 5y $$ is written as a product of three factors.
   - **Analysis:** The expression is a sum of terms, not a product. It cannot be factored into three factors.
   - **Conclusion:** False.

4. **Statement:** $$ 5 $$ is a coefficient.
   - **Analysis:** A coefficient is a numerical factor in a term. In the term $$ 5y $$, the number $$ 5 $$ is indeed the coefficient of $$ y $$.
   - **Conclusion:** True.

5. **Statement:** $$ 2x + 1 + 5y $$ is written as a sum of three terms.
   - **Analysis:** The expression consists of three distinct terms: $$ 2x $$, $$ 1 $$, and $$ 5y $$.
   - **Conclusion:** True.

6. **Statement:** None of these are true.
   - **Analysis:** Since some statements are true, this statement is false.
   - **Conclusion:** False.

### Summary of True Statements:
- $$ 1 $$ is a constant.
- $$ 5 $$ is a coefficient.
- $$ 2x + 1 + 5y $$ is written as a sum of three terms.

Thus, the true statements are:
- $$ 1 $$ is a constant.
- $$ 5 $$ is a coefficient.
- $$ 2x + 1 + 5y $$ is written as a sum of three terms.
The true statements are: - $$ 1 $$ is a constant. - $$ 5 $$ is a coefficient. - $$ 2x + 1 + 5y $$ is written as a sum of three terms.

Consider the following expression.

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Summary of True Statements:

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