Question

Use the area model to multiply 2(4a+7b+5).
First, find the partial products.
4a 7b 5
2
Row, rectangle. Width. Height. Find the total area.. Areacolumn, missing side length.1234
Now, write the product.
2(4a+

Answer 1

To multiply \( 2(4a + 7b + 5) \) using the area model, we'll break it down into partial products.

We start with the expression \( 4a + 7b + 5 \). The goal is to multiply each term in this expression by 2.

We can set up our area model as follows:

1. **Identify the terms:**
- The terms we have are \( 4a \), \( 7b \), and \( 5 \).

2. **Setup the area model:**

We'll create a table where one side represents the multiplier (2) and the other side represents the terms of \( 4a + 7b + 5 \):

\[
\begin{array}{c|c}
& 4a \quad 7b \quad 5 \\
\hline
2 & 2(4a) \quad 2(7b) \quad 2(5) \\
\end{array}
\]

3. **Calculate the partial products:**
- \( 2(4a) = 8a \)
- \( 2(7b) = 14b \)
- \( 2(5) = 10 \)

Now we have the partial products:

- From \( 4a \): \( 8a \)
- From \( 7b \): \( 14b \)
- From \( 5 \): \( 10 \)

4. **Combine the partial products:**

To find the total, we simply add the partial products together:

\[
8a + 14b + 10
\]

5. **Write the final product:**

Thus, the product of \( 2(4a + 7b + 5) \) is:

\[
\boxed{8a + 14b + 10}
\]