Question

Use the area model to multiply 7(5a+8b+9c).
First, find the partial products.
5a 8b 9c
7
Row, rectangle. Width. Height. Find the total area.. Areacolumn, missing side length.1234
Now, write the product.

Answer 1

To use the area model to multiply \( 7(5a + 8b + 9c) \), we'll break it down into its components and find the partial products.

### Step 1: Set up the area model
We'll create a grid where we multiply each term in the expression \( 5a + 8b + 9c \) by \( 7 \).

```
5a 8b 9c
+------------------------
7 | 35a | 56b | 63c |
+-------------------------
```

### Step 2: Calculate the partial products
Now we’ll find the partial products from the grid:

1. \( 7 \times 5a = 35a \)
2. \( 7 \times 8b = 56b \)
3. \( 7 \times 9c = 63c \)

### Step 3: Write down the total area
To find the total area, we sum all the partial products we calculated:

\[
35a + 56b + 63c
\]

### Final Product
Thus, the product of \( 7(5a + 8b + 9c) \) can be written in expanded form as:

\[
7(5a + 8b + 9c) = 35a + 56b + 63c
\]

This is the final result of multiplying \( 7 \) by the expression \( 5a + 8b + 9c \) using the area model.