My question today is whether or not it is in mathematical convention to do the following when expanding brackets.
If we have the expression $(x+2)(x-5)$ and we expand this out, we get $x^2-3x-10$. Would it go against mathematical convention to write this as $-3x+x^2-10$.
Thank you.
Addition is commutative, meaning that the order in which we add things does not matter, so $$x^2-3x-10\equiv x^2-10-3x\equiv-10+x^2-3x \equiv -3x-10+x^2 \equiv -3x+x^2-10.$$
So, to conclude, whatever floats your boat, in this case. Although, generally, it's more pleasing to the eye to write polynominals with the highest power first ($ax^n+bx^{n-1}+cx^{n-2}+\cdots$), then going down by one power, so I, personally, would write it as $x^2-3x-10$, but, again, whatever helps you is fine.
