Observe the figure, it is contain one triangle and one square.
\The base of the triangle is
.
The height of the triangle is
.
The area of the triangle is
.


Rewrite as the sum of two products.
\
Apply distributive property:
.


The length of the side of the square is
.
The area of the big square is
.

Apply square of a difference formula:
.
.
The area of shaded region is
.


Group like terms.
\
combine like terms.
\
.
The area of shaded region is
.