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
\[ -x + 1 \]
Polynomials
When writing a polynomial on its own, the usual convention is to write the terms in decreasing order of degree:
\[ x^3 - 32x^2 + 3x -1 \]
But for a series expansion, where higher-order powers are often omitted, it makes more sense to start with the lowest-degree term:
\[ -1 + 3x - 32x^2 + x^3 \]
