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Galina-37 [17]
3 years ago
6

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?
Mathematics
1 answer:
musickatia [10]3 years ago
7 0

Answer:

4x^2 + 22x + 15

Step-by-step 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

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