FOIL the following expressions.
`(x+7)(3+x)`

Answer

To FOIL the expression \((x + 7)(3 + x)\), we will follow the steps of the FOIL method, which stands for First, Outside, Inside, and Last.

### Step-by-Step Solution:

1. **Identify the terms**:
- The first expression is \(x + 7\).
- The second expression is \(3 + x\).

2. **Apply the FOIL method**:
- **First**: Multiply the first terms of each binomial:
\[ x \cdot x = x^2 \]

- **Outside**: Multiply the outer terms:
\[ x \cdot 3 = 3x \]

- **Inside**: Multiply the inner terms:
\[ 7 \cdot x = 7x \]

- **Last**: Multiply the last terms of each binomial:
\[ 7 \cdot 3 = 21 \]

3. **Combine all the results**:
- Now, we combine all the products obtained from the FOIL method:
\[ x^2 + 3x + 7x + 21 \]

4. **Combine like terms**:
- Combine the \(3x\) and \(7x\):
\[ 3x + 7x = 10x \]
- Therefore, the expression simplifies to:
\[ x^2 + 10x + 21 \]

### Final Answer:
\[ x^2 + 10x + 21 \]