Timeline for Why unlike terms cannot be simplified?
Current License: CC BY-SA 3.0
28 events
| when toggle format | what | by | license | comment | |
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| Oct 29, 2023 at 19:28 | answer | added | Luke Nemeth | timeline score: 0 | |
| Dec 23, 2015 at 6:59 | answer | added | varunk | timeline score: 0 | |
| Dec 18, 2015 at 19:53 | comment | added | Daniel R. Collins | Here's a question: Did you formally prove why combining like terms does work (using whatever axioms are in play for your class; for an elementary algebra class it's about 3 lines)? If so, then which step fails to hold for the case of unlike terms? | |
| Dec 18, 2015 at 16:43 | comment | added | Andrew | @MichaelE2 I don't follow. You say "$x^2+3xy^2+4xy+7x^2y$ seems a bit non-sensical in that if I let $x$ and $y$ be physical quantities" and "The expression makes sense for any numbers." Which is it? | |
| Dec 18, 2015 at 14:07 | comment | added | Andrew | @MichaelE2 If $x$ and $y$ are lengths, the polynomial is certainly sensible- it's the sum of the area of a square of length $x$, thrice the volume of a rectangular prism whose height is $x$ with a square base of side length $y$, four times the area of a rectangle with width $x$ and length $y$, and seven times the volume of a rectangular prism whose height is $y$ with a square base of side length $x$. For the rule, suffices to say that only geometric objects with identical dimensions can be combined. | |
| Dec 18, 2015 at 14:01 | comment | added | Andrew | @DagOskarMadsen Well, it is obvious, but not to a grade schooler who doesn't understand that polynomials form an infinite dimensional vector space whose basis is given by monomial products of the indeterminants- that's the point. | |
| Dec 18, 2015 at 3:17 | answer | added | Pieter Rousseau | timeline score: 0 | |
| Dec 17, 2015 at 16:59 | answer | added | mweiss | timeline score: 1 | |
| Dec 17, 2015 at 13:36 | answer | added | JTP - Apologise to Monica | timeline score: 4 | |
| Dec 16, 2015 at 3:27 | comment | added | mweiss | @DagOskarMadsen Phrased that way, the issue seems (at part) to be the conflation of "polynomial" (as a formal expression) and "polynomial function". You may find mathoverflow.net/questions/160986/… relevant. | |
| Dec 16, 2015 at 2:18 | answer | added | Jason | timeline score: 2 | |
| Dec 16, 2015 at 1:46 | comment | added | Dag Oskar Madsen | By the way I think this is a great question. Something that is taken as granted in school turns out not to be so obvious. | |
| Dec 16, 2015 at 1:33 | comment | added | Dag Oskar Madsen | If such a simplification existed for some expression, you could always move all terms to one side of the equation, so your question is equivalent to: "Why is a non-zero polynomial never identical to zero?" | |
| Dec 15, 2015 at 22:24 | review | Close votes | |||
| Dec 16, 2015 at 2:44 | |||||
| Dec 15, 2015 at 21:26 | answer | added | DavidButlerUofA | timeline score: 1 | |
| Dec 15, 2015 at 21:18 | answer | added | user52817 | timeline score: 2 | |
| Dec 15, 2015 at 21:07 | answer | added | Benoît Kloeckner | timeline score: 13 | |
| Dec 15, 2015 at 20:16 | answer | added | Jasper | timeline score: 0 | |
| Dec 15, 2015 at 19:44 | comment | added | mweiss | Part of the reason this is a hard question to respond to is because your counterexample seems unnecessarily complicated and arbitrary. What is the crux of the problem? Would you be satisfied with an explanation of why $4x + 2x^2$ can't be "simplified" to a single term? Is it important that there be two variables in the expression? If so, would you be satisfied with an explanation of why $4x + 3y$ can't be combined into a single term? Or do there need to be higher-degree combinations? In other words, can you delineate for what kinds of expressions you think students require an explanation? | |
| Dec 15, 2015 at 18:55 | history | edited | Behzad | CC BY-SA 3.0 |
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| Dec 15, 2015 at 18:44 | comment | added | Behzad | @MichaelE2 Well, when they asked so, I asked them back "Let's simplify it. What's your suggestion?" and disproved their suggestions by giving $x$ and $y$ appropriate values. I'm not looking for a proof. An explanation is enough. | |
| Dec 15, 2015 at 18:22 | answer | added | user6104 | timeline score: 1 | |
| Dec 15, 2015 at 18:17 | answer | added | Jasper | timeline score: 0 | |
| Dec 15, 2015 at 17:05 | history | edited | celeriko | CC BY-SA 3.0 |
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| Dec 15, 2015 at 17:01 | review | Close votes | |||
| Dec 15, 2015 at 17:56 | |||||
| Dec 15, 2015 at 16:49 | comment | added | Behzad | @BenoîtKloeckner I've just added an example. Is it clear enough now? | |
| Dec 15, 2015 at 16:46 | history | edited | Behzad | CC BY-SA 3.0 |
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| Dec 15, 2015 at 16:31 | history | asked | Behzad | CC BY-SA 3.0 |