Final answer:
The polynomial that represents the difference of the areas of a rectangle (shape A) and a square (shape B) involves calculating the area of both shapes and subtracting the area of the square from the rectangle. The area of the rectangle is found by multiplying the length by the width, and the square's area is found by squaring the side length.
Step-by-step explanation:
To find the polynomial that represents the difference of the areas of shape A and shape B, we have to calculate the area of both shapes and then subtract the area of shape B from the area of shape A.
Shape A is a rectangle with a length of 7x² + 4x + 8 and a width of 3x² + 2. To find its area, we multiply the length by the width:
Area of Rectangle A = (7x² + 4x + 8) * (3x² + 2)
Shape B is a square with a side length of 3x² + 2. To find its area, we square the side length:
Area of Square B = (3x² + 2) * (3x² + 2)
To find the difference between the area of rectangle A and the area of square B, we subtract the area of square B from the area of rectangle A:
Difference in Areas = Area of Rectangle A - Area of Square B
This gives us the polynomial:
Difference in Areas = (7x² + 4x + 8) * (3x² + 2) - (3x² + 2) * (3x² + 2)
Hence, the correct polynomial that represents the difference of the areas is the one that contains the subtraction of these two products, which is not explicitly given among the options provided. The steps taken to find the difference in areas involve algebraic multiplication and subtraction.