Explain to me how to prove pythagorean theoream?

Actually, in order to solve the Theorem, You have to look at the diagram:

You can see, Side of Square is (a+b)
So, Area = a * b = (a+b)(a+b)

Now, Area of Smaller square under the square = c²

There are four Triangles, their Area will be: 4(1/2ab) = 2ab

Now, Area under the square will be equivalent to the Total area of Square itself which is the same thing.

So, (a+b)(a+b) = c² + 2ab
a² + 2ab + b² = c² + 2ab 
Subtract 2ab from both sides, 
a² + b² = c²
[ Hence, Proved ]

Hope this helps!