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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 \(11(6 - 5r)\).