Final answer:
The area of the shaded region is -x² + 14x - 15 square inches.
Step-by-step explanation:
To find the area of the shaded region, we need to subtract the area of the smaller rectangle from the area of the larger rectangle. The area of the larger rectangle is given as 2x² + 4x - 7 square inches, and the area of the smaller rectangle is (3x+4)(x-2) square inches.
To find the area of the shaded region, we can subtract the area of the smaller rectangle from the area of the larger rectangle:
Shaded area = Area of larger rectangle - Area of smaller rectangle
Shaded area = (2x² + 4x - 7) - (3x+4)(x-2)
Simplifying the expression:
Shaded area = 2x² + 4x - 7 - (3x²- 2x - 8x +8)
Shaded area = 2x² + 4x - 7 - 3x² +10x -8
Shaded area = -x² + 14x - 15
Therefore, the area of the shaded region is -x² + 14x - 15 square inches.