The length of a side of a rectangle is 2 units less than a number, and the width is 4 units more than the length. Which of the following expressions represents the area of the rectangle, in square units?

A. x^2+2x+4
B. x^2-2x+8
C. x^2-4
D. x^2+4

x = a number

L = x - 2

W = L + 4 = x - 2 + 4 = x + 2

A = L * W =

( x - 2 ) * ( x + 2 ) =

x ^ 2 - 2 ^ 2 =

x ^ 2 - 4

Answer C

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Remark:

( a - b ) ( a + b ) = a ^ 2 - b ^ 2
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To find the expression that represents the area of the rectangle, we need to understand the relationship between its dimensions and the given information.

Let's assume the number in question is represented by x.

According to the given information:
- The length of the rectangle is 2 units less than x, which can be expressed as (x - 2).
- The width of the rectangle is 4 units more than the length, which can be expressed as ((x - 2) + 4) or (x + 2).

The area of a rectangle is calculated by multiplying its length and width. Therefore, the area can be represented as:

Area = Length × Width
Area = (x - 2) × (x + 2)
Area = x^2 - 2x + 2x - 4
Area = x^2 - 4

Hence, the expression that represents the area of the rectangle is x^2 - 4. Therefore, the answer is option C.