Observe the figure, it is contain one big square and one small square.
\The length of the side of the big square is
.
The area of the big square is
.

Apply square of sum formula:
.
.
The length of the side of the small 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
.