Write a new expression in simplest form that represents the difference between the areas of two different rectangles, rectangle A and rectangle B, given that the length of rectangle A is 3x+4 and the width is 5x-2, while rectangle B has a length of 2x+3 and a width of 4x+1. Then, determine the exact difference in area between the two rectangles when x=2.

To find the difference in area between two rectangles, we need to subtract the area of one rectangle from the area of the other rectangle.

Let's start by finding the area of rectangle A. The formula for the area of a rectangle is length multiplied by width. So, the area of rectangle A is (3x+4) * (5x-2).

Next, we will find the area of rectangle B. The area of rectangle B is (2x+3) * (4x+1).

To determine the exact difference in area between the two rectangles when x=2, we will substitute x=2 into the expressions we found for the areas of the rectangles.

Area of rectangle A: (3*2+4) * (5*2-2) = 10 * 8 = 80
Area of rectangle B: (2*2+3) * (4*2+1) = 7 * 9 = 63

Finally, to find the exact difference in area, we subtract the area of rectangle B from the area of rectangle A.

Difference in area = Area of rectangle A - Area of rectangle B
Difference in area = 80 - 63
Difference in area = 17 square units

Therefore, the exact difference in area between the two rectangles when x=2 is 17 square units.