Answer:
shaded area = 9x² +10x +4
Explanation:
The area of the shaded region is the difference between the areas of the overall rectangle and the unshaded one it contains. Each area is the product of length and width.
Rectangle areas
Overall rectangle
A = LW
A = (5x)(3x) = 15x² . . . . . using given dimensions
Unshaded interior rectangle
A = (3x +1)(2x -4) = 3x(2x -4) +1(2x -4) . . . . . using given dimensions
A = 6x² -12x +2x -4 = 6x² -10x -4
Difference of areas
The shaded area is the difference between the area of the overall rectangle and the area of the unshaded included rectangle.
shaded area = (15x²) -(6x² -10x -4)
shaded area = 9x² +10x +4