@Obliv Figures that when I ask for help I'm kicked out where I got the question.
Anyways, I've got another one. Its involving finding difference, but as I've learned its a trick. I got this far with the problem, the invisible 1 changed some of the signs. $-2d^3 + 6d - 9 + 7d^2 - 5d - 13$ Originally it was $(-2d^3 + 6d - 9) - (-7d^2 + 5d + 13)$. I got this far alone and want to confirm my thought process, so I'd like a second opinion.
the core principle with polynomial arithmetic is recognizing what the monomials are. in one variable d, that's powers of d, in a multivariable setting it is subtler.
the addition is defined so that you can "collect" like monomials and "add their coefficients." but none of this is well-posed without a lot of background understanding. "6a^4 b^4 +(8a^4 b^4 - 9b)" is not in anyway disqualified as an answer to an ill-formed question that just asks you to "add" those polynomials
same reason that "31 - 26/2" is a perfectly good response to "what's 31 - 26/2." specifying the form of an answer to the question is 99% of the question.
Were I to give a similar question to my students, the instruction would likely be something like "Simplify the following polynomial expression so that there is only one of any term of the form $Ca^m b^n$, where $C$ is a real number, and $m$ and $n$ are natural numbers."
I would need to word smith that a bit more, as it is a bit hard to grok, but I think that the general intention of the question is to get you to "combine like terms".
In other news, it is currently 77°F inside. Is it time to turn on the AC?
@YourLordJoyBoy Yeah so you basically distribute the minus sign. Also the first parentheses is just another implicit $1(...)$ so we just have $-2d^3+6d-9-1(-7d^2+5d+13)=-2d^3+6d-9+(-1)(-7)d^2+(-1)(5)d+(-1)(13) = -2d^3+6d-9+7d^2-5d-13)$
Actually, I would probably give the instruction "Rewrite the polynomial in standard form," where "standard form" is something that would have been discussed previously in class---roughly, write the terms in order of decreasing degree, and if two terms have the same degree, write them in lexicographical order; no two terms should contain precisely the same combination of variables, i.e. collect "like terms").
@XanderHenderson I believe that was in standard form, the final answer I mean. And now I'm doing a similar one, and trying to combine $9/7z with 15z$. Other than that the problem is cake.
