Question

or
Use the area model to factor 66–55r.
First, find the terms of the missing factor.
11 66
–
55r
Row, rectangle. Width. Height. Find the total area.. Areacolumn, missing side length.123
Now, write 66–55r in factored form.

Answer 1

To factor the expression \(66 - 55r\) using the area model, let's first identify the components involved.

### Step 1: Identify Common Factors

We can start by looking for the greatest common factor (GCF) of the coefficients. The coefficients here are 66 and -55.

- The factors of 66 are \(1, 2, 3, 6, 11, 22, 33, 66\).
- The factors of 55 are \(1, 5, 11, 55\).

The GCF of 66 and 55 is \(11\).

### Step 2: Factor Out the GCF

Now, let's factor \(66 - 55r\) by taking out the GCF, which is \(11\):

\[
66 - 55r = 11(6 - 5r)
\]

### Step 3: Area Model Representation

To visualize this, you can think of it in terms of an area model.

- The total area represents the expression \(66 - 55r\).
- You can think of one rectangle with a width of \(11\) and a height that we need to determine.

The area of this rectangle can be described by:

\[
\text{Area} = \text{Width} \times \text{Height}
\]

Given the area is \(66 - 55r\) and the width is \(11\):

\[
11 \times \text{Height} = 66 - 55r
\]

To find the height, we divide \(66 - 55r\) by \(11\):

\[
\text{Height} = \frac{66}{11} - \frac{55r}{11} = 6 - 5r
\]

### Final Expression in Factored Form

Putting it all together, we have factored \(66 - 55r\) to get:

\[
66 - 55r = 11(6 - 5r)
\]

Thus, the factored form of \(66 - 55r\) is **\(11(6 - 5r)\)**.