What is the purpose of the Distributive law in this proof? (From Spivak)

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So I'm reading Spivak Calculus and it makes sense. But, what I can't understand is, what is the purpose of the following:

$$\begin{align}13\cdot4 &= (1\cdot10 + 3)\cdot4\\&= 1\cdot10\cdot4 + 3\cdot4\\&= 4\cdot10 + 12\\&= 4\cdot10 + 1\cdot10 + 2\\&= (4 + 1)\cdot10 + 2\\&= 5\cdot10 + 2\\&= 52\end{align}$$

Could anyone please explain?