Question

Write an expression that represents the area of the garden.

Area = (
)(
)

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:
a

Answer 1

To find the expression that represents the area of the garden, we’ll use the given dimensions in the area model, which appears to be based on a rectangle with two pairs of sides.

**Part A: Expression for the area**

The dimensions of the garden are provided as:
- Height (one side): \(2x - 4\)
- Width (other side): \(3x + 7\)

Thus, the area \(A\) can be expressed as:
\[
A = (2x - 4)(3x + 7)
\]

---

**Part B: Finding the area using the area model**

To find the area, we will expand the expression \( (2x - 4)(3x + 7) \) using the distributive property (also known as FOIL—in this case, First, Outside, Inside, Last):

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

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

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

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

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

Next, combine like terms:
\[
A = 6x^2 + (14x - 12x) - 28 = 6x^2 + 2x - 28
\]

---

**Part C: The simplified polynomial written in standard form**

The simplified polynomial representing the area of the garden in standard form is:
\[
A = 6x^2 + 2x - 28
\]

Thus, the answer for part C is:

\[
a = 6x^2 + 2x - 28
\]