### What is the cube of the algebraic binomial?

The binomial cube is a volume puzzle, enclosed in a small wooden box. The binomial cube concretely represents the algebraic formula (a + b) ^ 3 = (a + b) x (a + b) x (a + b). With a, the edge of the blue cube, b, the edge of the red cube, for example.

The lid has (a + b) 2, the cube has (a + b) 3.

Example with the cover:

(a + b) 2 = (a + b) * (a + b)

= a * a + a * b + b * a + b * b

= a2 (blue square) + 2ab (the 2 black rectangles) + b2 (red square)

Development with the cube works according to the same principles.

This material makes it possible to develop the perception of different proportions in the three dimensions and thus to develop the mathematical sense of the child.

### How to present the binomial cube?

The box is deposited in front of the child. It is necessary to place the box so that the two moving sides open precisely forwards and to the right.

On the lid is painted the image of the upper face of the binomial. So, open each side, one after the other, observing the correspondence between the actual cube and the lid.

We then begin to dismantle the cube, layer by layer, by grouping on the table the parallelepipeds by sizes, shapes and colors. Cubes have two colors: black and red or black and blue. There is also a cube “all red” and a cube “all blue”.

Show the child that the lid needs to be observed to recompose the cube. We will begin by placing the big cube “all red” and then, we will place the following cubes of the same layer according to this simple principle: color against color. For example, against the big cube “all red”, we will stick on each side a red and black cube by making the red faces coincide.

Once the cube is finished, we close the box: it is the moment of **control of the error.**

In a second presentation, when the child has already practiced well, we can show him how to make the cube just on the lid or even directly on the table.