Which function models the area of a rectangle with side lengths of 2x - 4 units x - 1 units

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Answer:

The function which models the area of the rectangle is A (x) = 2x² - 6x + 4

Step-by-step explanation:

The formula of the area of a rectangle is A = l w, where l is its length and w is its width

∵ The length of a rectangle is (2x - 4) units

∵ The width of the rectangle is (x - 1) units

- Use the formula of area to find its area

∵ A = l w

∴ A = (2x - 4) (x - 1)

Let us multiply the two brackets

∵ (2x - 4) (x - 1) = (2x) (x) + (2x) (-1) + (-4) (x) + (-4) (-1)

∴ (2x - 4) (x - 1) = 2x² + (-2x) + (-4x) + 4

- Add the like terms

∴ (2x - 4) (x - 1) = 2x² + (-6x) + 4

∴ (2x - 4) (x - 1) = 2x² - 6x + 4

Write A as a function of x

∵ The area of the rectangle is A (x)

∵ The area of the rectangle is 2x² - 6x + 4

∴ A (x) = 2x² - 6x + 4

The function which models the area of the rectangle is A (x) = 2x² - 6x + 4