Consider the following expression. $$ \begin{array}{l}7(1+3)(2 b+9) \ \text { Select all of the true statements below. } \ \square 7 \text { is a factor. } \ \square(2 b+9) \text { is written as a sum of three terms. } \ \square 1 \text { and } 3 \text { are like terms. } \ \square \text { In } 2 b, 2 \text { is a coefficient. } \ \square \text { In }(2 b+9), 2 b \text { is a constant. } \ \square \text { None of these are true. }\end{array} $$

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UpStudy AI · Accepted Answer

$$7(1+3)(2b+9)$$ is an expression written as a product of three factors. We now analyze each statement one by one.

1. **"7 is a factor."**

The number $$7$$ is written as a multiplier in the expression. Hence, $$7$$ is indeed one of the factors.  
   **True.**

2. **"$$(2b+9)$$ is written as a sum of three terms."**

The expression $$(2b+9)$$ consists of two terms: $$2b$$ and $$9$$.  
   **False.**

3. **"1 and 3 are like terms."**

In the term $$(1+3)$$, both $$1$$ and $$3$$ are constant numbers. Constants are considered like terms since they do not contain any variables.  
   **True.**

4. **"In $$2b$$, 2 is a coefficient."**

In the term $$2b$$, the number $$2$$ multiplies the variable $$b$$, which by definition makes $$2$$ the coefficient of $$b$$.  
   **True.**

5. **"In $$(2b+9)$$, $$2b$$ is a constant."**

The term $$2b$$ contains the variable $$b$$ and is not a constant.  
   **False.**

6. **"None of these are true."**

Since we have found that some of the statements (statements 1, 3, and 4) are true, this statement is incorrect.  
   **False.**

Thus, the true statements are:

- $$7$$ is a factor.
- $$1$$ and $$3$$ are like terms.
- In $$2b$$, $$2$$ is a coefficient.
The true statements are: - 7 is a factor. - 1 and 3 are like terms. - In 2b, 2 is a coefficient.

Consider the following expression.

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