Question

What is the area of the shaded region in the diagram below? Express your answer in factored form.

Answer 1

There are 2 squares in the picture, one with sides length of x, and another one with sides length of 8.

The area of the shaded region is obtained by subtracting the areas of these two squares.

The area of a square is calculated as follows:

`A=s^2`

where s is the length of the sides.

The area of the external square is:

`A_1=x^2`

The area of the internal square is:

`A_2=8^2`

Therefore, the area of the shaded region is:

`\begin{gathered} A=A_1-A_2 \\ A=x^2-8^2 \\ which\text{ is a difference of squares, then:} \\ A=(x-8)(x+8) \end{gathered}`