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 vividly demonstrates, in a tangible way, the well-established algebraic truth that *x^3 – y^3 = (x-y)(x^2+xy+y^2)*. While it is entirely feasible to show that the equation holds true in a physical context, it pushes the boundaries of physical modeling. The elegant algebraic manipulation might be more aesthetically pleasing. That's why we still rely on algebra. The key concepts explored 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)* cubic units; (2) the three solids *x^2(x-y), xy(x-y), and y^2(x-y)* can be skillfully arranged into a *x^3* minus *y^3*, as depicted in the images. A box is included to facilitate the arrangement of the blocks for the *(x^2+xy+y^2)* base. It's entirely irrelevant how these three pieces are laid out on the floor as long as one can clearly 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 exploring!