If a rectangle has a length of (2x−3)(2𝑥−3) and a width of (2x+3)(2𝑥+3) , what is the area of the rectangle? Write your answer in standard form.
Question
If a rectangle has a length of (2x−3)(2𝑥−3) and a width of (2x+3)(2𝑥+3) , what is the area of the rectangle? Write your answer in standard form.
Solution
The area of a rectangle is calculated by multiplying its length by its width.
So, for a rectangle with length (2x-3) and width (2x+3), the area (A) would be:
A = (2x-3) * (2x+3)
This is a multiplication of two binomials, which can be solved using the FOIL method (First, Outer, Inner, Last).
First: 2x * 2x = 4x^2 Outer: 2x * 3 = 6x Inner: -3 * 2x = -6x Last: -3 * 3 = -9
Adding these together gives:
A = 4x^2 + 6x - 6x - 9 A = 4x^2 - 9
So, the area of the rectangle is 4x^2 - 9.
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