Why multiply first?

This is just a notational convention to allow one of the expressions $$(a+b)\cdot c\qquad a+(b\cdot c) $$be written without parentheses. One could have chosen the other (or to always require parentheses), but think how complicated it would make writing e.g. polynomials (unless written as product of linear factors). The same considereation holds for why $a-b-c$ stands for $(a-b)-c$ and not for $a-(b-c)$. Alternatively, one might introdue a prefix ore postfix (instead of infix) notation, aka. (reverse) Polish notation, i.e. $ab+c\cdot$ or $\cdot +abc$ vs. $abc\cdot+$ or $+a\cdot bc$.

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Algebra Precalculus

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