Question

Part B: Use the area model to find the area of the garden.

3x 7
2x
-4
Part C: The simplified polynomial written in standard form is:

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Answer 1

To find the area of the garden using the area model, we can represent the dimensions of the garden as a rectangle where one side is represented by \( (2x - 4) \) and the other side is represented by \( (3x + 7) \).

### Step 1: Set Up the Area Model

We have the following dimensions:
- Length: \( 2x - 4 \)
- Width: \( 3x + 7 \)

### Step 2: Multiply the Polynomial Expressions

To find the area, we need to multiply these two expressions:

\[
(2x - 4)(3x + 7)
\]

### Step 3: Apply the Distributive Property (FOIL Method)

1. **First**: Multiply the first terms:
\[
2x \cdot 3x = 6x^2
\]

2. **Outer**: Multiply the outer terms:
\[
2x \cdot 7 = 14x
\]

3. **Inner**: Multiply the inner terms:
\[
-4 \cdot 3x = -12x
\]

4. **Last**: Multiply the last terms:
\[
-4 \cdot 7 = -28
\]

### Step 4: Combine All the Products

Now, we combine all these results:
\[
6x^2 + 14x - 12x - 28
\]

### Step 5: Simplify the Polynomial

Combine the like terms:
\[
6x^2 + (14x - 12x) - 28 = 6x^2 + 2x - 28
\]

### Final Result

Thus, the simplified polynomial written in standard form is:
\[
\boxed{6x^2 + 2x - 28}
\]

This is the area of the garden expressed as a polynomial in standard form.