(a+b)³

thingiverse

This is a 3D representation of the binomial theorem. The cube can be made by adding the components: (a+b)^3 = a^3 + 3a^2b + 3ab^2 + b^3 This was created with FreeCAD and Inkscape for the fonts. Print Settings Printer: Prusa i3 Rafts: Doesn't Matter Supports: No Resolution: 0.2 Infill: 20% Notes: Quantities: 1 a^3 3 a^2b 3 ab^2 1 b^3 Standards: NGSS, CCSS Overview and Background Physical representation of the binomial theorem It can be accompanied by a graphical representation on the blackboard of the square (a+b)^2 that can be formed with its components. And then show the distributive, to confirm that it forms a perfect cube. Lesson Plan and Activity Deductive thinking The activity would start by showing the components separately, identifying the size of "a" and the size of "b". Then invite kids to form a regular figure with all the pieces. When you reach the cube, make the sum of all the edges, demonstrating that it is a cube of side (a+b)(a+b)(a+b) => (a+b)^3. Then on the blackboard starting from (a+b)^3 apply the distributive to arrive at the expression that gives rise to cubes and rectangular prisms.