Write a polynomial expression in simplest form that represents the difference between the area of the larger rectangle and the area of the smaller rectangle. Then find the difference when x=4.
Assistance needed.
Is the small one in the big one or what?
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To find the difference between the area of the larger rectangle and the area of the smaller rectangle, we need to determine the areas of both rectangles and then subtract the two.
Let's assume the larger rectangle has length L and width W, while the smaller rectangle has length (L-2x) and width (W-2x). Here, x represents a variable.
The area of the larger rectangle is given by A1 = L * W.
The area of the smaller rectangle is given by A2 = (L-2x) * (W-2x).
To find the polynomial expression representing the difference in area, we subtract A2 from A1:
Difference = A1 - A2.
So, the polynomial expression is:
Difference = (L * W) - ( (L-2x) * (W-2x) ).
Now, let's find the difference when x=4:
Substitute x=4 into the polynomial expression above, and calculate the value of the difference.
Difference (when x=4) = (L * W) - ( (L-2(4)) * (W-2(4)) ).
Simplifying further:
Difference (when x=4) = (L * W) - ( (L-8) * (W-8) ).
Please note that without specific values for L and W, we cannot determine the exact value of the difference. However, you can substitute any values for L and W into the polynomial expression above to find the difference when x=4.