Question

The side length of a square is represented by the expression 2x + 5. Which expression represents the difference between the area of the square and the perimeter of the square?

Answer 1

`4x^2 + 22x + 15`

Explanation:

The side length of a square is represented by the expression 2x + 5.

The area of a square is given as:

`A = a^2`

where a = length of side of the square

The area of the square is therefore:

`A = (2x + 5)^2\\\\A = (2x + 5)(2x + 5)\\\\A = 4x^2 + 20x + 25`

The perimeter of a square is given as:

`P = 4a`

The perimeter of the square is therefore:

`P = 4(2x + 5) \\\\P = 8x + 10`

The difference between the area of the square and the perimeter of the square is:

`4x^2 + 30x + 25 - (8x + 10)\\\\4x^2 + 30x + 25 - 8x - 10\\\\4x^2 + 30x - 8x + 25 -10\\\\4x^2 + 22x + 15`

The expression that represents the difference between the area and the perimeter of the square is:

`4x^2 + 22x + 15`