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If the side length of a square could be given with the expression (2x + 5) what expression could represent its area

User Porjaz
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Final answer:

The area of a square with a side length expressed as (2x + 5) is given by the polynomial 4x² + 20x + 25, which is obtained by squaring the expression (2x + 5).

Step-by-step explanation:

If the side length of a square is represented by the expression (2x + 5), then to find the area of the square, we would square this expression. Squaring a number means to multiply it by itself. So, the area of the square would be:

Area = (side length) · (side length) = (2x + 5) · (2x + 5)

By expanding this expression (using a method such as FOIL), we get:

Area = 4x² + 20x + 25

This polynomial represents the area of the square in terms of x. The coefficient 4 is the square of the 2 in (2x), the middle term 20x is twice the product of 2x and 5, and 25 is the square of 5.

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