Geometrical demostration of notable product (a + b)^2

Hello my friends on steemit, this is my first publication totally written in english and also is my first little article dedicated to science, specifically Mathematics and I wanted to start with something very common in algebra: the notable product.

We start considering two squares, one having equals sides labeled with the letter a, and its area is calculated by multiplying the sides: area = a x a = a^2 (see fiure 1)

(Figure 1)

The second square has sides labeled with letter b and its area, just like the other square will be b^2 (figure 2)

(Figure 2)

Next we will constuct two equals rectangles but with the following features: base = a, height = b and area = a x b (figure 3)

(Figure 3)

Now, we will put together all quadrilaterals to form one big square with sides equal to a + b (figure 4)

(Figure 4)

The area of this square we can compute as we know, multiplying side by side: (a + b) x (a + b) = (a + b)^2, but this multiplication is equal to the sumatory of the areas of each quadrilaters:
a^2 + b^2 + ab + ab.

Now, rearranging and placing both equalities we obtain the result we know

(a + b)^2 = a^2 + 2ab + b^2

In conclusion, we obtain a very well-known formula used in algebra from geometry, demostrating that all mathematics is derivated from geometry.

Reference: Algebra, Aurelio Baldor.