Difference of Two Cubes: x^3 – y^3 = (x-y)(x^2+xy+y^2)

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####*x^3 –y^3 = (x-y)(x^2+xy+y^2)* ##### Physical Model for the Difference of Two Cubes This set of 3D blocks demonstrate, physically, the well-known algebraic fact that *x^3 – y^3 = (x-y)(x^2+xy+y^2)*. While it is possible to show that the equation is true in a physical sense, it is a bit of a stretch toward physical modeling. The algebraic manipulation might be more aesthetically appealing. That is why we still need algebra. The big ideas covered are: (1) If the area of a polygon is *(x^2+xy+y^2)* square units, then, when extended (or extruded) for *(x-y)* units in the 3rd dimension, the resulting solid has a volume of *(x-y)(x^2+xy+y^2)*; (2) the three solids *x^2(x-y), xy(x-y), and y^2(x-y)* can be arranged into a *x^3* minus *y^3*, as shown in the pictures. A box is also included for help with the arrangement of the blocks for the *(x^2+xy+y^2)* base. Of course, it does not matter how these three pieces are laid out on the floor as long as one can identify the three terms, *x^2, xy, and y^2*. By the way, **what is the volume of the interior of the box**? Have fun!