Visualising polynomials: cube of a binomial

In this activity you will prove the formula for the cube of a binomial by using both algebra and geometry.
Make a set of solids (8 in total) using some clay or cardboard. [br][br][list][list=1][*]Make a cube of side a.[br][/*][*]Make a cube of side b.[br][/*][*]Make 3 rectangular prisms of side (a x a x b).[br][/*][*]Make 3 rectangular prisms of side  (a x b x b). [br][/*][*]Use all of these 3-D shapes to make a cube.[/*][*]You can help yourself using the applet below.[br][/*][/list][/list][list][br][/list][br][br]
What is the side of the larger cube, the yellow one?
Write the formula for the cube of a binomial
[math]\left(a+b\right)^3=?[/math]
In the previous question you might have used algebra to give the formula. Now use geometry to provide the same formula. Use your 3D model or the applet above.
What happens if b is a negative number?You can use the simulation below for your reasoning.
Chiudi
– Jennifer Silverman, sonom, Gara Szabolcs, lorena gazzola

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