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------------------------------------------------ A rectangular wall is [tex]4x - 5[/tex] units high and [tex]2x + 7[/tex] units long. Which polynomial best represents the area of the wall in square units?

A. [tex]8x^2 - 18x - 35[/tex]
B. [tex]8x^2 + 38x + 35[/tex]
C. [tex]8x^2 - 38x + 35[/tex]
D. [tex]8x^2 + 18x - 35[/tex]

The area of a rectangle is found by multiplying its length by its width. The polynomial representing the area of the wall in this case is 8x² + 18x - 35, which is obtained by multiplying the binomials (4x - 5) and (2x + 7) and simplifying.

Explanation:

To find the area of a rectangle, we multiply its length by its width. The rectangle in question has dimensions 4x – 5 (height) and 2x + 7 (length). So, the polynomial representing the area in square units is obtained by multiplying these two linear expressions:

Area = (4x – 5) × (2x + 7)

The multiplication of two binomials can be done using the distributive property (also known as the FOIL method – First, Outside, Inside, Last):

Area = (4x × 2x) + (4x × 7) + (-5 × 2x) + (-5 × 7)

Area = 8x² + 28x - 10x - 35

Simplifying the like terms (28x - 10x) gives:

Area = 8x² + 18x - 35

Therefore, the correct answer is option D: 8x² + 18x - 35.