Final answer:
The area of the shaded rectangle is (2x+6)(2x-6), which simplifies to 4x^2 - 36.
Step-by-step explanation:
The expression for the area of the shaded rectangle is given by multiplying the length and width of the rectangle. The length is 2x+6 and the width is 2x-6. Therefore, the area is (2x+6)(2x-6).
You can simplify the expression by applying the distributive property. First, multiply 2x by 2x to get 4x^2. Then, multiply 2x by -6 to get -12x. Next, multiply 6 by 2x to get 12x. Finally, multiply 6 by -6 to get -36. Combine like terms to get a completely simplified expression for the area of the shaded rectangle: 4x^2 - 12x + 12x - 36.
Simplifying further, the expression becomes 4x^2 - 36, which is the completely simplified expression for the area of the shaded rectangle.