Question

find the area of the shaded region

Explanation:

Step1: Calculate area of outer square

The outer shape is a square with side length $x+1$. Area of a square is side length squared.
$\text{Area}_{\text{outer}} = (x+1)^2 = x^2 + 2x + 1$

Step2: Calculate area of inner rectangle

The inner shape is a rectangle with length $x-7$ and width 5. Area of a rectangle is length $\times$ width.
$\text{Area}_{\text{inner}} = 5(x-7) = 5x - 35$

Step3: Subtract inner area from outer area

Shaded area = outer area minus inner area.
$\text{Area}_{\text{shaded}} = (x^2 + 2x + 1) - (5x - 35)$
Simplify the expression:
$\text{Area}_{\text{shaded}} = x^2 + 2x + 1 - 5x + 35 = x^2 - 3x + 36$

Answer:

$x^2 - 3x + 36$