The order of terms matters even when they commute
From Why start at x, y, z
When writing an expression that consists of several terms, the conventions regarding their order appear arbitrary.
Multiplication
It is usual to write:
- \(xy\) and \(yx\) in either order;
- \(5t\) but not \(t5\) (to avoid confusion with \(t_5\) or \(t^5\));
- \(x\sqrt{2}\) but not \(\sqrt{2}x\) (to avoid confusion with \(\sqrt{2x}\)). (See Something on the right of a radical)
- \(\sqrt{2}\sin x\) but not \(\sin x \sqrt{2}\) (to avoid confusion with \(\sin \left(x\sqrt{2}\right)\)).
Addition
People sometimes rearrange a sum to avoid a leading unary minus, even when this contradicts the convention of writing terms in decreasing order of degree:
\[ 1 - x \]
instead of
\[ -x + 1 \]
