Question

Use the area model to multiply 4(10+5u).
First, find the partial products.
10 5u
4
Row, rectangle. Width. Height. Find the total area.. Areacolumn, missing side length.123
Now, write the product.

Answer 1

To use the area model to multiply \( 4(10 + 5u) \), we will break it down into parts and then find the total area by calculating the partial products.

### Step 1: Set up the area model

We can think of \( 10 + 5u \) as a rectangle that has a width of \( 10 + 5u \) and a height of \( 4 \).

### Step 2: Create rows for partial products

We will create two rows: one for \( 10 \) and one for \( 5u \).

| | 10 | 5u |
|-------------|--------|--------|
| **4** | | |

### Step 3: Calculate Partial Products

1. **For the width 10:**
\[
4 \times 10 = 40
\]

2. **For the width 5u:**
\[
4 \times 5u = 20u
\]

### Step 4: Fill in the table with the partial products

| | 10 | 5u |
|-------------|--------|--------|
| **4** | 40 | 20u |

### Step 5: Find the total area

To find the total area, we add the partial products together:
\[
40 + 20u
\]

### Step 6: Write the final product

Thus, the product of \( 4(10 + 5u) \) is:
\[
\boxed{40 + 20u}
\]