Answer
(a.) $ x^2-4y^2$.
(b.) $(x+2y)(x-2y)$.
Work Step by Step
The formula for the area of the square is $A=(length)^2$.
Length of the bigger square is $x$.
Area of the bigger square is $A_1=x^2$.
Length of the smaller four squares is $y$.
Area of the one smaller square is $=(y)^2$.
Total area of the four smaller squares is $A_2=4y^2$.
(a.) An expression for the area of the shaded blue region is $=A_1-A_2$
$ = x^2-4y^2$.
(b.) The expression is:
$ = x^2-(2y)^2$.
Use the algebraic identity.
$a^2-b^2=(a+b)(a-b)$
$x^2-(2y)^2=(x+2y)(x-2y)$.
