Final answer:
The area of the rectangular courtyard with length (3x + 5) and width (2x - 3) is best represented by the expression 6x² + x - 15, found by multiplying the length and width and combining like terms.
Step-by-step explanation:
The expression that best represents the area of the rectangular courtyard, with length (3x + 5) and width (2x - 3), is found by multiplying the length and the width. To find the area of a rectangle, the formula is length × width. So we will multiply these two expressions: (3x + 5)(2x - 3).
Multiplying these two binomials, we get:
- 3x × 2x = 6x^2
- 3x × -3 = -9x
- 5 × 2x = 10x
- 5 × -3 = -15
Combining like terms (-9x + 10x = x), the expression simplifies to:
6x^2 + x - 15