Answer
a. $x^{2}+2xy+y^{2}$
b. $(x+y)(x+y)$
Work Step by Step
a. Area of the shaded region = (Area of the square whose side is x ) + 2 (Area of the rectangle whose sides are x,y) + (Area of the small square whose side is y)
$= x^{2} + 2(xy) + y^{2}$
$= x^{2} + 2xy + y^{2}$
b. In factored form
The factor $ x^{2} + 2xy + y^{2}$ has three terms and is a perfect square trinomial. Factor using $ A^{2} + 2AB + B^{2} = (A+B)^{2}$
$ x^{2} + 2xy + y^{2} = (x+y)^{2}$
$= (x+y)(x+y)$
