Sum of Two Cubes: Physical Models

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This set of 3D blocks visually demonstrates, in a hands-on way, that *x^3 + y^3 = (x+y)(x^2 - xy + y^2)*. The equation is easy to prove physically, but it's also possible to show the algebraic manipulation is more visually appealing. The big ideas covered are: (1) When you extend a polygon with an area of *(x^2 - xy + y^2)* square units for *(x+y)* units in the third dimension, the resulting solid has a volume of *(x+y)(x^2-xy+y^2)*; (2) The four solids *x^2(x-y), xy(x-y), xy^2, and y^3* can be arranged into two cubes: *x^3* and *y^3*, as shown in the pictures. Note that the term *(-xy)* is represented by the missing piece at the bottom. A box is included to help with the arrangement of blocks for the *(x^2 - xy + y^2)* base. The height of the box is *(x+y)*.