Question

Enter the missing values in the area model to find 5, left parenthesis, 3, n, minus, 3, right parenthesis5(3n−3)

Answer 1

To find the product of \( 5(3n - 3) \) using an area model, we can break down the expression into manageable parts.

First, we need to factor or distribute the expression \( 3n - 3 \):

1. **Factor out the common term:**
\( 3n - 3 = 3(n - 1) \)

2. **Rewrite the expression:**
Now we can rewrite the original expression as:
\[ 5(3(n - 1)) = (5 \cdot 3)(n - 1) = 15(n - 1) \]

### Area Model Representation

You can visualize this using an area model as follows:

- Create a rectangle split into two parts: one for \( 5 \cdot 3n \) and another for \( 5 \cdot (-3) \).

- Break down the calculations:

#### Breakdown of Area Model:
- **First rectangle (for \( 3n \) part):**
One side will be \( 5 \) and the other will be \( 3n \), giving you an area of \( 15n \).

- **Second rectangle (for \( -3 \) part):**
One side will still be \( 5 \) and the other side will be \( -3 \), giving you an area of \( -15 \).

### Area Model Summary
The area model can be represented as:

\[
\begin{array}{|c|c|}
\hline
5 & -15 \\
\hline
15n & -15 \\
\hline
\end{array}
\]

### Final Result
The final result when combining the areas is:

\[
15n - 15
\]
So, \( 5(3n - 3) = 15n - 15 \).

This is the complete simplified form of the expression using an area model to organize the terms.