Question

Use the area model to multiply 10(6p+1).
First, find the partial products.
6p 1
10
Row, rectangle. Width. Height. Find the total area.. Areacolumn, missing side length.123
Now, write the product.
10(6p+1)=

Answer 1

To multiply \(10(6p + 1)\) using the area model, we first break down the expression \(6p + 1\) into its components and set up the multiplication:

### Step 1: Set Up the Area Model
We'll represent the multiplication as a rectangle where one side has a length of 10 and the other side is divided into the parts of \(6p + 1\):

- Width of the rectangle: \(10\)
- Height of the rectangle: Two parts, \(6p\) and \(1\)

### Step 2: Create Partial Products
Now, we calculate the area for each part of the rectangle:

1. **Area for \(6p\)**:
\[
10 \times 6p = 60p
\]

2. **Area for \(1\)**:
\[
10 \times 1 = 10
\]

### Step 3: Add the Partial Products
Next, we add the partial products together to find the total area:

\[
60p + 10
\]

### Step 4: Write the Final Product
Thus, the product of \(10(6p + 1)\) is:
\[
10(6p + 1) = 60p + 10
\]