<u>Given</u>:
The length of the entire rectangle is 10x + 7.
The width of the entire rectangle is 6x.
The length of the unshaded rectangle is 4x - 5.
The width of the unshaded rectangle is 2x.
We need to determine the area of the shaded region of the rectangle.
<u>Area of the entire rectangle:</u>
The area of the entire rectangle can be determined using the formula,
Substituting the values, we have;
Thus, the area of the entire rectangle is 60x² + 42x
<u>Area of the unshaded rectangle:</u>
The area of the unshaded rectangle can be determined using the formula,
Substituting the values, we have;
Thus, the area of the unshaded rectangle is 8x² - 10x
<u>Area of the shaded region of the rectangle:</u>
The area of the shaded region of the rectangle can be determined by subtracting the area of the entire rectangle by the area of the unshaded rectangle.
Thus, we have;
Thus, we have;
Thus, the area of the shaded region of the rectangle is 52x(x + 1)