Answer
(a) $(x+y)^2$
(b) $x^2+y^2+2xy$
(c) They represent the same area.
(d) $(x+y)^2=x^2+2xy+y^2$
Work Step by Step
(a) Based on the given conditions, we have the area of the largest square as: $A=(x+y)(x+y)=(x+y)^2$
(b) The two small squares are $A_1=x^2, A_2=y^2$, the area of the two rectangles are $A_3=A_4=xy$. Thus the total is $A=x^2+y^2+2xy$
(c) They are equivalent because they represent the same area.
(d) The formula is $(x+y)^2=x^2+2xy+y^2$
