Question

Use the area model to multiply 7(3+3k).
First, find the partial products.
3 3k
7
Row, rectangle. Width. Height. Find the total area.. Areacolumn, missing side length.123
Now, write the product.
7(3+3k)=

Answer 1

To use the area model to multiply \( 7(3 + 3k) \), we can break it down step by step.

1. **Create the area model**: We think of \( 3 + 3k \) as a rectangle where one side is \( 3 \) and the other side is \( 3k \). So, we can visualize this as:

- Width: \( 3 \)
- Height: \( 3k \)

2. **Set up the multiplication**:
We can distribute the \( 7 \) across each term in the parenthesis:

\[
7(3 + 3k) = 7 \cdot 3 + 7 \cdot 3k
\]

3. **Calculate the partial products**:
- \( 7 \cdot 3 = 21 \)
- \( 7 \cdot 3k = 21k \)

4. **Combine the partial products**:
Now we add the partial products together:

\[
21 + 21k
\]

5. **Write the product**:
Therefore, the final product is:

\[
7(3 + 3k) = 21 + 21k
\]

Thus, the product \( 7(3 + 3k) \) simplifies to \( 21 + 21k \).