Question

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

3x 7 lenghth
2x
-4 width
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 given the dimensions, we can use the dimensions provided:

Length of the garden = \(3x + 7\)

Width of the garden = \(2x - 4\)

#### Part B: Finding the Area

The area \(A\) of a rectangle is given by the formula:
\[
A = \text{Length} \times \text{Width}
\]

Substituting the given expressions for length and width:
\[
A = (3x + 7)(2x - 4)
\]

Now, we can use the distributive property (FOIL method) to expand this expression:

1. First multiply \(3x\) by each term in the second binomial \( (2x - 4) \):
\[
3x \cdot 2x = 6x^2
\]
\[
3x \cdot (-4) = -12x
\]

2. Next, multiply \(7\) by each term in the second binomial \( (2x - 4) \):
\[
7 \cdot 2x = 14x
\]
\[
7 \cdot (-4) = -28
\]

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

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

#### Part C: Standard Form

The simplified polynomial written in standard form is:
\[
A = 6x^2 + 2x - 28
\]

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