Why doesn’t (x+y) ^2 equal x^2+y^2 ? [Great way to demonstrate exponential growth in a simple way!] – re-post from Quora

Answer by Viktor Toth:

Others provided you with the algebra and explained that exponentiation does not distribute over addition, but here is a way to think about this in terms of geometry:

This is a square with sides that have lengths of x+y. Clearly, the area of the square is (x + y)^2. But it is also equal to the sum of the areas of the shapes inside: A square with area x^2, another square with area y^2, and two rectangles, with area xy. The total comes to x^2 + y^2 + 2xy.

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