A rectangular park is 6x + 2 ft long and

3x + 7 ft wide. In the middle of the park is

a square turtle pond that is 8 ft wide. What

expression represents the area of the park not

occupied by the turtle pond? SEE EXAMPLE 6

18x^2 + 48x - 50

Step-by-step explanation: In order to determine the area of the rectangle not covered by the turtle pond, we shall calculate the area of the square pond and subtract it from the area of the rectangle.

The area of the square is given as

Area = L x B, where A and B are of equal measurement (sides of a square)

Area = 8 x 8

Area = 64 ft^2

Next we calculate the area of the rectangle which is given as

Area = L x B, where L = 6X + 2 and W = 3X + 7

Area = (6X + 2) (3X +7)

Area = 18X^2 + 42X + 6X + 14

Area = 18X^2 + 48X + 14

We can now subtract the area of the square from the area of the rectangle

That is Area of the shaded region

= 18X^2 48X + 14 - 64

= 18X^2 + 48X - 50

Therefore, the area of the shaded region = 18X^2 + 48X - 50