+2666 Make a diagram like this:
The area of the entire square is \((a+b)^2 = a^2 + b^2 + 2ab\)
The area can also be represented as the sum of the area of the 4 triangles and the square in the middle: \(c^2 + 2ab\)
Since they both represent the area of the square, we have the equation \(a^2 + b^2 + 2ab = c^2 + 2ab\)
Subtracting 2ab from both sides gives us \(\color{brown}\boxed{a^2 + b^2 = c^2}\)
