Mathematical Memorandum: My favorite formula

I had a mathematical chat with some friends in the last month. One of them said, "My favorite formula is partial fraction decomposition":
$\frac{1}{x(x - 1)} = \frac{x - (x - 1)}{x(x - 1)} = \frac{1}{x - 1} - \frac{1}{x},$

and the other one said, "I like the integration by parts formula":
$\int f(x) g^{'}(x) \textrm{d} x = f(x) g(x) - \int f^{'}(x) g(x) \textrm{d} x.$

These two formula have a common point: they follow from an idea
$0 = - X + X.$

Indeed, the first formula obviously follows from this idea. The second formula also follows, since we have the differentiation of product-type functions from the definition of differentiation as follows.
$\begin{array}{cl} & \displaystyle{ \{ f(x) g(x) \}^{'} } \\ \notag =& \displaystyle{\lim_{h \to 0} \frac{f(x + h) g(x + h) - f(x) g(x)}{h}} \\ \notag =& \displaystyle{\lim_{h \to 0} \frac{f(x + h) g(x + h) - f(x + h) g(x) + f(x + h) g(x) - f(x) g(x)}{h}} \\ \notag =& \displaystyle{f (x) \lim_{h \to 0} \frac{g(x + h) - g(x)}{h} + \lim_{h \to 0} \frac{f(x + h) - f(x)}{h} g (x)} \\ \notag =& \displaystyle{f (x) g^{'} (x) + f^{'} (x) g (x)} \\ \notag \end{array}$

My favorite mathematical formula is this simplest one:
$(a - b)^2 = a^2 - 2ab + b^2.$

Once we understand the true meaning of this formula, we immediately obtain many formulas including the relation between arithmetic means and geometric means, Schwarz's inequality and the upper bound of symmetric forms.

My favorite formula

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