Express the area of the entire rectangle.

Question

Expression should be expanded.
An area model for a rectangle with a height of three x and a width of two x minus three. The rectangle is broken into two rectangles to isolate each term in the width. The first rectangle has a height of three x and a width of two x. The second rectangle has a height of three x and a width of negative three.

Answer 1

To find the area of the rectangle based on the given dimensions, we start with the height and width.

1. Height of the rectangle: \( h = 3x \)
2. Width of the rectangle: \( w = 2x - 3 \)

The area \( A \) of a rectangle is calculated using the formula:

\[ A = \text{Height} \times \text{Width} \] Substituting the given values:

\[ A = (3x)(2x - 3) \]

To find the expanded form, we can distribute \( 3x \) across the width:

\[ A = 3x \cdot 2x + 3x \cdot (-3) \]

Calculating each term:

• \( 3x \cdot 2x = 6x^2 \)
• \( 3x \cdot (-3) = -9x \)

Now, combining these results gives us:

\[ A = 6x^2 - 9x \]

Thus, the area of the rectangle, expressed in expanded form, is:

\[ \boxed{6x^2 - 9x} \]