Question

Use the area model to multiply 4(20d+12).
First, find the partial products.
20d 12
4
Row, rectangle. Width. Height. Find the total area.. Areacolumn, missing side length.123
Now, write the product.
4(20d+12

Answer 1

To multiply \( 4(20d + 12) \) using the area model, we can break it down into partial products based on the distribution of \( 4 \) over the terms in the parentheses:

1. **Create the area model:**
- We split \( 20d + 12 \) into its two parts: \( 20d \) and \( 12 \).
- The product can be visualized as a rectangle where one side (width) is \( 4 \) and the other side (height) represents the two segments: \( 20d \) and \( 12 \).

2. **Calculate the partial products:**
- **For the first section**:
\[
4 \times 20d = 80d
\]
- **For the second section**:
\[
4 \times 12 = 48
\]

3. **Write the total area by combining the partial products**:
\[
80d + 48
\]

4. **Final expression**:
So, the product of \( 4(20d + 12) \) is:
\[
80d + 48
\]

Thus, using the area model, we found that \( 4(20d + 12) \) equals \( 80d + 48 \).