Question

Use the area model to multiply 4(8r+11+3s).
First, find the partial products.
8r 11 3s
4
Row, rectangle. Width. Height. Find the total area.. Areacolumn, missing side length.1234
Now, write the product.
4(8r+11+3s)=

Answer 1

To multiply \( 4(8r + 11 + 3s) \) using the area model, we'll break it down as follows:

1. **Identify the terms to multiply**:
\[
4 \text{ will be multiplied by each term in } (8r + 11 + 3s).
\]

2. **Set up the area model with partial products**:

We can represent this multiplication like a rectangle where one side (height) is \( 4 \) and the other side (width) represents the three terms \( (8r, 11, 3s) \):

```
| 8r | 11 | 3s |
----------------------------------
4 | 32r | 44 | 12s |
```

3. **Calculate the partial products**:
- For \( 8r \):
\[
4 \times 8r = 32r
\]
- For \( 11 \):
\[
4 \times 11 = 44
\]
- For \( 3s \):
\[
4 \times 3s = 12s
\]

4. **Sum the partial products**:
Combine all the partial products to find the total area:
\[
32r + 44 + 12s
\]

5. **Write the final product**:
Putting it all together, we have:
\[
4(8r + 11 + 3s) = 32r + 44 + 12s
\]

So, the final result is:
\[
\boxed{32r + 44 + 12s}
\]