A Geometric Model of (a+b)2-The Infinity Mathematics

 

A Geometric Model of (a+b)².

           Introducing (a+b)² . Although most, not all, algebra students accept and use the expansions for(a+b)², many students have difficulty conceptualizing these products. The following introductory expository organizer, presented in the form of a demonstration will make these products more meaningful for many students.      

        Being the demonstration by selecting two arbitrary lengths a and b and demonstrating that the geometric representations of a² and b² are squares having dimensions a by a and b by b, respectively. Next, consider the lengths a+b, and construct a square of dimension (a+b) by (a+) as a geometric representation of (a+b)² .Then compare the square having side (a+b) to the two squares having side a and b, respectively. The geometric representations of a², b², and (a+b)² are illustrated below in figure 1.

                                Figure 1: A Geometric Model of (a+b)².