[Tex/LaTex] How to typeset subquestions and the corresponding answers

answersexamexercisespackagesprobsoln

I would like to typeset exercises with subquestions so that in the code I have an answer immediately following each subquestion, but in the output all the answers will be in the end. Also I want both exercises and subquestions to be automatically numbered. I know that there are several packages for typesetting exercises (for example 'answers', 'exercise' and 'probsoln'). I also know that there is a document type called 'exam'.

My question is: Which package would work best for this and what kind of code would produce the result?

I would like to write something like the following:

\begin{ExerciseList}
  \Exercise{}
    Calculate the following:
    \Question{$7+2$}
      \Answer{$9$}
    \Question{$9-9$}
      \Answer{$0$}
    \Question{$5+5+5$}
      \Answer{$15$}
  \Exercise{}
    Solve the following equations:
    \Question{$x+5=7$}
      \Answer{$x=2$}
    \Question{$x-5=9$}
      \Answer{$x=14$}
    \Question{$5x=20$}
      \Answer{$x=4$}
\end{ExerciseList}

And I wan the final document look something like this:

Exercise 1
Calculate the following:
a) 7+2 b) 9-9
c) 5+5+5

Exercise 2
Solve the following equations:
a) x+5=7 b) x-5=9 c)
5x=20

Solutions:

Exercise 1
a) 9 b) 0 c) 15

Exercise 2
a) x+5=7 b) x=14 c) x=4

The code that I have above is just an example. The commands do not have to be exactly as I have written as long as the structure is similar.

Best Answer

With the probsoln package, problems can be defined either within the document or in an external file that can be loaded using a command such as \loadallproblems or \loadrandomproblems.

Here's a simple example with the problems defined in the document:

\documentclass{article}

\usepackage{probsoln}

\begin{defproblem}{prob1}% label
  \begin{onlyproblem}% question
    Calculate the following:%

    \begin{textenum}
    \item $7+2$
    \item $9-9$
    \item $5+5+5$
    \end{textenum}
  \end{onlyproblem}%
  \begin{onlysolution}% solution
    \begin{textenum}
    \item $9$
    \item $0$
    \item $15$
    \end{textenum}
  \end{onlysolution}
\end{defproblem}

\begin{defproblem}{prob2}% label
  \begin{onlyproblem}% question
    Solve the following equations:

    \begin{textenum}
    \item $x+5=7$
    \item $x-5=9$
    \item $5x=20$
    \end{textenum}
  \end{onlyproblem}%
  \begin{onlysolution}% solution
    \begin{textenum}
    \item $x=2$
    \item $x=14$
    \item $x=4$
    \end{textenum}
  \end{onlysolution}
\end{defproblem}

\begin{document}
\renewcommand{\labelenumii}{\theenumii)}

\begin{enumerate}
\foreachproblem{\item\thisproblem}
\end{enumerate}

\section*{Solutions}

\showanswers
\begin{enumerate}
\foreachsolution{\item\thisproblem}
\end{enumerate}

\end{document}

This produces

Image of document showing problems and the solutions

The formatting can be changed. For example, using the enumitem package:

\documentclass{article}

\usepackage{probsoln}
\usepackage{enumitem}

\begin{defproblem}{prob1}% label
  \begin{onlyproblem}% question
    Calculate the following:%

    \begin{textenum}
    \item $7+2$
    \item $9-9$
    \item $5+5+5$
    \end{textenum}
  \end{onlyproblem}%
  \begin{onlysolution}% solution
    \begin{textenum}
    \item $9$
    \item $0$
    \item $15$
    \end{textenum}
  \end{onlysolution}
\end{defproblem}

\begin{defproblem}{prob2}% label
  \begin{onlyproblem}% question
    Solve the following equations:

    \begin{textenum}
    \item $x+5=7$
    \item $x-5=9$
    \item $5x=20$
    \end{textenum}
  \end{onlyproblem}%
  \begin{onlysolution}% solution
    \begin{textenum}
    \item $x=2$
    \item $x=14$
    \item $x=4$
    \end{textenum}
  \end{onlysolution}
\end{defproblem}

\newenvironment{ExerciseList}
{\begin{enumerate}[label={\emph{Exercise \arabic*}},%
   ref={\arabic*},wide]
  \renewcommand{\labelenumii}{\theenumii)}%
}
{\end{enumerate}}

\newcommand{\exercise}{\item\mbox{}\par}

\begin{document}

\begin{ExerciseList}
\foreachproblem{\exercise\thisproblem}
\end{ExerciseList}

\section*{Solutions}

\showanswers
\begin{ExerciseList}
\foreachsolution{\exercise\thisproblem}
\end{ExerciseList}

\end{document}

This produces:

Image of resulting document

Edit:

Here's an alternative where you can write the answer next to the question in the code:

\documentclass{article}

\usepackage{probsoln}
\usepackage{enumitem}

\newcommand{\QA}[2]{%
  \begin{onlyproblem}#1\end{onlyproblem}%
  \begin{onlysolution}#2\end{onlysolution}}

\begin{defproblem}{prob1}% label
  \begin{onlyproblem}% question
    Calculate the following:%

  \end{onlyproblem}%
  \begin{textenum}
    \item \QA{$7+2$}{$9$}
    \item \QA{$9-9$}{$0$}
    \item \QA{$5+5+5$}{$15$}
  \end{textenum}
\end{defproblem}

\begin{defproblem}{prob2}% label
  \begin{onlyproblem}% question
    Solve the following equations:

  \end{onlyproblem}%
  \begin{textenum}
    \item \QA{$x+5=7$}{$x=2$}
    \item \QA{$x-5=9$}{$x=14$}
    \item \QA{$5x=20$}{$x=4$}
  \end{textenum}
\end{defproblem}

\newenvironment{ExerciseList}
{\begin{enumerate}[label={\emph{Exercise \arabic*}},%
   ref={\arabic*},wide]
  \renewcommand{\labelenumii}{\theenumii)}%
}
{\end{enumerate}}

\newcommand{\exercise}{\item\mbox{}\par}

\begin{document}

\begin{ExerciseList}
\foreachproblem{\exercise\thisproblem}
\end{ExerciseList}

\section*{Solutions}

\showanswers
\begin{ExerciseList}
\foreachsolution{\exercise\thisproblem}
\end{ExerciseList}

\end{document}

The result is the same as the previous example.

Edit 2:

Here's a method that defines and displays the problem. The label is generated automatically:

\documentclass{article}

\usepackage{probsoln}
\usepackage{enumitem}

\newcommand{\QA}[2]{%
  \begin{onlyproblem}#1\end{onlyproblem}%
  \begin{onlysolution}#2\end{onlysolution}}

\newenvironment{ExerciseList}
{\begin{enumerate}[label={\emph{Exercise \arabic*}},%
   ref={\arabic*},wide]
  \renewcommand{\labelenumii}{\theenumii)}%
}
{\end{enumerate}}

\newcommand{\exercise}{\item\mbox{}\par}

\newcommand{\Exercise}[2]{\exercise 
 #1\par
 \begin{defproblem}{prob\arabic{enumi}}%
  \begin{textenum}%
  #2%
  \end{textenum}%
 \end{defproblem}%
 \useproblem{prob\arabic{enumi}}%
}

\begin{document}

\begin{ExerciseList}
 \Exercise{Calculate the following:}%
 {%
    \item \QA{$7+2$}{$9$}
    \item \QA{$9-9$}{$0$}
    \item \QA{$5+5+5$}{$15$}
 }%

 \Exercise{Solve the following equations:}
 {%
    \item \QA{$x+5=7$}{$x=2$}
    \item \QA{$x-5=9$}{$x=14$}
    \item \QA{$5x=20$}{$x=4$}
 }
\end{ExerciseList}

\section*{Solutions}

\showanswers
\begin{ExerciseList}
\foreachsolution{\exercise\thisproblem}
\end{ExerciseList}

\end{document}

Related Solutions

[Tex/LaTex] Please explain \Newassociation and provide an overview of how the package answers works

I agree that the documentation of the answers package is a bit on the terse side. I don't find the exercise documentation to be very difficult; it can do a lot of things, but is quite well documented, I think. I've never used probsoln so I won't comment further on that.

Since you ask about the answers package specifically, here is my attempt at explaining the package, and clarifying at least the simple example given in the documentation.

First, the basic command \Newassociation{xxx}{yyy}{zzz} does the following things:

It creates an environment {xxx} to be used in your document for the solutions within the problems themselves. This environment will generally not be displayed unless the [nosolutionfiles] option chosen when the package is loaded.
It creates an environment {yyy} which is the environment that will be used to display the solutions. These solutions are written to a separate file (or files) and then can be input into your document at a later place (e.g. at the end of a chapter, or at the end of the entire book.)
It creates a file naming schema for the solution file(s) based on zzz. Either a single file is used (in which case it will be zzz.tex) or multiple files are used, in which case zzz acts as a kind of label that identifies the type of solution it is, and the file names are given explicitly.

Because xxx, yyy and zzz are used as part of environment/macro names, they must only contain letters, since these are the only valid characters for multi-character macro names in TeX. As with other macro names, they are case-sensitive (Xxx ≠ xxx). Furthermore, you should make sure that they do not conflict with existing environments that you may have in your document.

In the documentation, there are three sample documents (ansexam{1|2|3}.tex) which show how this works in practice. I've taken the simple example here (ansexam1.tex), and annotated it with some comments. (On TeXLive distributions, these files can be found in /usr/local/texlive/2010/texmf-dist/doc/latex/answers/).

\documentclass[12pt,a4paper]{article}
% First we load the package.
\usepackage{answers}
% Now we set up a solution set.
% The environment that marks solutions within exercises is {sol}.
% The environment that marks solutions to be displayed is {Solution}
% The solution file type is "ans".
\Newassociation{sol}{Solution}{ans}

% Now we set up a theorem-like environment for exercises (this is)
% standard LaTeX; you could also use any of the more sophisticated
% theorem packages to do this.
\newtheorem{ex}{Exercise}

\begin{document}

% The next command opens a file to store the solutions. Without the second
% argument, the file would be called `ans.tex`.  With the second argument
% the file is called `ans1.tex` and it is of the "ans" type.
\Opensolutionfile{ans}[ans1]

% Now we write our problems, and for each problem we write its solution into the
% "sol" environment.  The solutions will not be displayed here.
\section{Problems}
\begin{ex}
   First exercise
   \begin{sol}
      First solution.
   \end{sol}
\end{ex}
\begin{ex}
   Second exercise
   \begin{sol}
      Second solution.
   \end{sol}
\end{ex}

% Now that we are done with our exercises and our solutions,
% we close the solution file
%
\Closesolutionfile{ans}

% Now our document has created a file called "ans1.tex" which contains a bunch of
% "Solution" environments, one for each "sol" environment that we put into the 
% exercises. This file can now be \input back into another place in the document,
% here in the section called "Solutions".

\section{Solutions}
\input{ans1}
\end{document}

If you run this document, you will find that it has created a file ans1.tex which looks like the following:

\begin{Solution}{1}
      First solution.

\end{Solution}
\begin{Solution}{2}
      Second solution.

\end{Solution}

The Solution environment is set up by the \Newassociation command. It has some basic formatting, which you can change as needed, either with hooks provided by the package, or by using \renewenvironment after you have issued the \Newassociation command.

For example, there is a hook \solutionstyle which formats the label of each solution. This is initially set to \bfseries, so the solution environment produces:

1 First solution

2 Second solution

You could redefine it as follows:

\renewcommand{\solutionstyle}[1]{\bfseries Answer to Exercise #1 }

And now your solutions would appear as:

Answer to Exercise 1 First solution

Answer to Exercise 2 Second solution

More complicated formatting is possible for any of the environments created using the yyy argument of the \Newassociation command. There are two hooks, \preyyy and \postyyy (in this example, this would be \preSolution and \postSolution.) These must be created using \newcommand by you, and will be prepended or appended to the output solution as needed. For example, if you wanted each solution to end with a bullet, you could use:

\newcommand\postSolution{\hfill\textbullet}

Which would result in a right aligned bullet on its own line (ugly, but just an example.)

If you want your solutions to be more fancily formatted, you would use \renewenvironment to define the environment the way you like.

[Tex/LaTex] Adding a section of answers for each section of exercises at the end of a book using answers package

A possible solution using the titlesec package to change the formatting for the sectional units and and explicit option to gain access to the title for the sectional units using #1 (refer to the package documentation); the fncychap package is no longer needed.

The modified file libro.cls (the code contains some comments):

\NeedsTeXFormat{LaTeX2e}[2009/09/24]
\ProvidesClass{libro}

\LoadClassWithOptions{book}
\RequirePackage[pdftex]{graphicx}
\RequirePackage[latin1]{inputenc}
\RequirePackage[spanish]{babel}
\RequirePackage{amsmath,amsfonts,amssymb,amsthm}
\RequirePackage{array}
\RequirePackage{fancyhdr}
\RequirePackage{afterpage}
\RequirePackage{thmtools}
\RequirePackage{multicol}
\RequirePackage{color}
\RequirePackage{import}
\RequirePackage[font=small]{caption}
\RequirePackage{float}
\RequirePackage{subfig}
\RequirePackage{ifthen}
\RequirePackage{calc}
\RequirePackage{remreset}
\RequirePackage{pb-diagram}
\RequirePackage[hidelinks]{hyperref}
\RequirePackage[capitalise,noabbrev,spanish]{cleveref}
\RequirePackage{answers}

\renewcommand\paragraph{\@startsection
    {paragraph}{3}{0cm}             
    {6pt}                           
    {1pt}                           
    {\bfseries}}                    

\newcounter{cuentaEjercicios}[section]
\renewcommand{\thecuentaEjercicios}{\Alph{cuentaEjercicios}}
\declaretheoremstyle[%
  spaceabove=1em,%
  spacebelow=1em,%
  headfont=\normalfont,%
  postheadspace=1em,%
  headpunct={.}]{estiloDeEjercicio} 
 \declaretheorem[
    name={},
    style=estiloDeEjercicio,
    refname={Ejercicio},
    numberlike=cuentaEjercicios
]{ejer}

\newcounter{definicion}
\declaretheoremstyle[%
  spaceabove=6pt,%
  spacebelow=6pt,%
  headfont=\normalfont\bf,%
  notefont=\normalfont\bf,
  notebraces={{}{}},
  bodyfont=\itshape,
  headpunct={.}]{estiloDeDefinicion} 
 \declaretheorem[
    name={Definici\'on},
    numberlike=definicion,
    style=estiloDeDefinicion]{defi}

\RequirePackage[explicit]{titlesec}

% to store the chapter name
\newcommand\mychaptername{}
% to store the section name
\newcommand\mysectionname{}

% chapter formatting
\titleformat{\chapter}[display]
  {}{}{0pt}
  {\titlerule[0.5pt]\vspace{2ex}%
    \filleft{\LARGE\bfseries\chaptertitlename\ \thechapter.\space%
    \normalfont\LARGE#1}\gdef\mychaptername{#1}}
  [{\vspace{1ex}\titlerule[0.5pt]}]
\titleformat{name=\chapter,numberless}[display]
  {}{}{0pt}
  {\filleft\normalfont\LARGE#1}
  [{\vspace{1ex}\titlerule[0.5pt]}]
\titlespacing*{\chapter}
  {0pt}{20pt}{40pt}

% change section formatting in chapters 2,3,...
\let\leo@chapter\chapter
\renewcommand{\chapter}{
  \ifnum\value{chapter}>0 
    \changesectionanddefi 
    \let\chapter\leo@chapter
  \fi
    \leo@chapter
}

% format for sections in chapter 1 
\titleformat{\section}
  {\normalfont\bfseries}{\thesection}{0.5em}
  {#1\gdef\mysectionname{#1}}%

% format for sections in chapters 2,3,... 
\newcommand\changesectionanddefi{%
\titleformat{\section}
  {\normalfont\Large}{\thesection}{0.5em}
  {##1\gdef\mysectionname{##1}%
   \@addtoreset{definicion}{section}%
   \renewcommand{\thedefi}{\thesection.\arabic{definicion}}%
}%
}
\titlespacing*{\section}
  {0pt}{3.5ex plus 1ex minus .2ex}{2.3ex plus .2ex}

\newcommand{\seccionDeEjercicios}{%
  \newpage%
  \kern 5mm
  \hrule
  \kern 3mm
  \null \hfill {\large Ejercicios~\thesection.\space\mysectionname}\par
  \kern 3mm
  \hrule
  \kern 5mm
  \ifnum\value{section}=1 \relax
    \Writetofile{solucionario}{\protect\paragraph*{\chaptername\space\thechapter.\space\mychaptername}}
  \else\fi
  \Writetofile{solucionario}{\protect\paragraph*{Ejercicios\space\thesection.
  \space\mysectionname}}
}


\newcommand{\Z}{\ensuremath{\mathbb{Z}}}
\newcommand{\R}{\ensuremath{\mathbb{R}}}
\newcommand{\N}{\ensuremath{\mathbb{N}}}
\newcommand{\Q}{\ensuremath{\mathbb{Q}}}
\newcommand{\nin}{\not \in}
\newcommand{\ds}[1]{\displaystyle{#1}}

\fancypagestyle{respuestas}{%
    \fancyhf{}%
    \fancyhead[LO]{\small\slshape Soluciones a los ejercicios}%           
    \fancyhead[RE]{\small\slshape Soluciones a los ejercicios}%          
     \fancyhead[LE,RO]{\thepage}}

\AtBeginDocument{
     \addtocontents{toc}{\protect\markboth{\small\textsl Contenidos}{\small\textsl 
    Contenidos}}
    \pagestyle{fancy}
    \fancyhf{}
    \renewcommand\headrulewidth{0pt}
    \renewcommand{\chaptermark}[1]{\markboth{#1}{}}     
    \renewcommand{\sectionmark}[1]{\markright{#1}{}}
    \fancyhead[LO]{\small\textsl{\leftmark}}            
    \fancyhead[RE]{\small\textsl{\rightmark}}           
    \fancyhead[LE,RO]{\thepage}                         
    \Opensolutionfile{solucionario}
    \Newassociation{respuesta}{Res}{solucionario}
    \renewcommand{\Res}[1]{\textbf{Ejercicio #1.}}
    \Writetofile{solucionario}{\protect\chapter*{Respuestas}}
    \Writetofile{solucionario}{\protect\pagestyle{respuestas}}
}

The test file, with the new code using titlesec:

\documentclass[12pt,letterpaper]{libro}

\usepackage[
%           showframe,
            headheight=14.5pt,text={14cm,21cm},centering
            ]{geometry}
\usepackage{enumerate}
\usepackage{cases}               


\parindent=0cm

\begin{document}

\chapter{Números Reales}
bla bla bla blabla blabla blabla blabla blabla blabla blabla blabla blabla blabla blabla 
bla bla bla blabla blabla blabla blabla blabla blabla blabla blabla blabla blabla blabla 
bla bla bla blabla blabla blabla blabla blabla blabla blabla blabla blabla blabla blabla
bla bla bla blabla blabla blabla blabla blabla blabla blabla blabla blabla blabla blabla 

\section{Propiedades de campo}

\seccionDeEjercicios
\begin{ejer}
Efectúe las operaciones indicadas. Exprese el resultado como un
polinomio reducido.
\begin{multicols}{2}
\begin{enumerate}
\item $\left( x+\dfrac{1}{2}\right) ^{2}$
\item $\left( 3-2x\right) ^{2}$
\item $\left( x-\dfrac{2}{3}\right) ^{3}$
\item $\left( 2-x\right) ^{3}$
\item $\left( 2x^{2}-\dfrac{1}{2}+x^{2}\right) ^{2}$
\item $\left( -x-y\right) ^{2}$
\item $\left( -x-y\right) ^{3}$
\item $\left( -x-2y-4x\right) ^{3}$
\item $-\left( 2x^{3}-3t^{3}\right) ^{2}$
\item $\left(-2+x^{2}-3c-x^{2}\right) ^{2}$
\item $\left( \dfrac{x+2u^{2}}{3}\right) ^{2}$
\item $-\left( \dfrac{x^{2}-u^{2}}{2}\right) ^{2}$
\item $\left( \left( x-r\right)^{2}-r^{2}\right) ^{2}$
\item $3\left( x-2t\right) ^{4}-3\left(2t-x\right) ^{4}$
\end{enumerate}
\end{multicols}

\begin{respuesta}
\begin{multicols}{2}
\begin{enumerate}
\item $x^{2}+x+\dfrac{1}{4}$ 
\item $4x^{2}-12x+9$ 
\item $ x^{3}-2x^{2}+\dfrac{4}{3}x-\dfrac{8}{27}$
\item $-x^{3}+6x^{2}-12x+8$
\item $ 9x^{4}-3x^{2}+\dfrac{1}{4}$
\item $ x^{2}+2xy+y^{2}$
\item $-x^{3}-3x^{2}y-3xy^{2}-y^{3}$
\item $-125x^{3}-150x^{2}y-60xy^{2}-8y^{3}$
\item $-9t^{6}+12t^{3}x^{3}-4x^{6}$
\item $9c^{2}+12c+4$
\item $\dfrac{4}{9}u^{4}+\dfrac{4}{9}u^{2}x+\dfrac{1}{9}x^{2}$
\item $-\dfrac{1}{4}u^{4}+\dfrac{1}{2}u^{2}x^{2}-\dfrac{1}{4}x^{4}$
\item $4r^{2}x^{2}-4rx^{3}+x^{4}$
\end{enumerate}
\end{multicols}
\end{respuesta}
\end{ejer}


\chapter{Álgebra}

\section{Operaciones con polinomios}
bla bla bla blabla blabla blabla blabla blabla blabla blabla blabla blabla blabla blabla 
bla bla bla blabla blabla blabla blabla blabla blabla blabla blabla blabla blabla blabla 
bla bla bla blabla blabla blabla blabla blabla blabla blabla blabla blabla blabla blabla 
bla bla bla blabla blabla blabla blabla blabla blabla blabla blabla blabla blabla blabla 

\seccionDeEjercicios
\begin{ejer}
Efectúe las operaciones indicadas. Exprese el resultado como un
polinomio reducido.
\begin{multicols}{2}
\begin{enumerate}
\item $\left( x+\dfrac{1}{2}\right) ^{2}$
\item $\left( 3-2x\right) ^{2}$
\item $\left( x-\dfrac{2}{3}\right) ^{3}$
\item $\left( 2-x\right) ^{3}$
\item $\left( 2x^{2}-\dfrac{1}{2}+x^{2}\right) ^{2}$
\item $\left( -x-y\right) ^{2}$
\item $\left( -x-y\right) ^{3}$
\item $\left( -x-2y-4x\right) ^{3}$
\item $-\left( 2x^{3}-3t^{3}\right) ^{2}$
\item $\left(-2+x^{2}-3c-x^{2}\right) ^{2}$
\item $\left( \dfrac{x+2u^{2}}{3}\right) ^{2}$
\item $-\left( \dfrac{x^{2}-u^{2}}{2}\right) ^{2}$
\item $\left( \left( x-r\right)^{2}-r^{2}\right) ^{2}$
\item $3\left( x-2t\right) ^{4}-3\left(2t-x\right) ^{4}$
\end{enumerate}
\end{multicols}

\begin{respuesta}
\begin{multicols}{2}
\begin{enumerate}
\item $x^{2}+x+\dfrac{1}{4}$ 
\item $4x^{2}-12x+9$ 
\item $ x^{3}-2x^{2}+\dfrac{4}{3}x-\dfrac{8}{27}$
\item $-x^{3}+6x^{2}-12x+8$
\item $ 9x^{4}-3x^{2}+\dfrac{1}{4}$
\item $ x^{2}+2xy+y^{2}$
\item $-x^{3}-3x^{2}y-3xy^{2}-y^{3}$
\item $-125x^{3}-150x^{2}y-60xy^{2}-8y^{3}$
\item $-9t^{6}+12t^{3}x^{3}-4x^{6}$
\item $9c^{2}+12c+4$
\item $\dfrac{4}{9}u^{4}+\dfrac{4}{9}u^{2}x+\dfrac{1}{9}x^{2}$
\item $-\dfrac{1}{4}u^{4}+\dfrac{1}{2}u^{2}x^{2}-\dfrac{1}{4}x^{4}$
\item $4r^{2}x^{2}-4rx^{3}+x^{4}$
\end{enumerate}
\end{multicols}
\end{respuesta}
\end{ejer}


\begin{ejer}
Determine el cociente y el residuo en cada caso.

\begin{enumerate}
\item $\left( 2x^{3}-x^{2}+2x-1\right) \div \left( x-2\right) $
\item $\left( 4x^{3}+2x^{2}-3x-5\right) \div \left( 2x-1\right) $
\item $\left( x^{8}+x^{6}+x^{4}-x^{2}+x\right) \div \left( x-3\right) $
\item $\left( x^{4}-x^{3}-x^{2}+x^{3}+1\right) \div \left( -x+1\right) $
\item $\left( x^{3}+x^{6}+2x^{5}-\dfrac{x^{2}}{2}+x\right) \div \left(x-1\right) $
\end{enumerate}
\end{ejer}

\newpage

\begin{ejer}
Efectúe las operaciones indicadas. Exprese el resultado como un
polinomio reducido.

\begin{enumerate}
\item $-(7x^{2}+3x-4)+(8-x^{2}+5x^{3})-(2x^{3}+3x^{2}-5+8x)$
\item $\left( 11x^{3}-x+7\right) -\left( 2x-4x^{3}-6\right) +\left(7x^{2}-9x+4\right) $
\item $\left( x^{2}+2xy+4y^{2}\right) \left( x-2y\right) $
\item $5a^{3}b^{2}\left( ab^{2}-b+4a\right) -(8a^{3}b^{3}-10a^{4}b^{4})$
\item $(3x^{2}-8x+7)(x^{3}+x)+(2x^{3}-6x+2)$
\item $\dfrac{-36x^{2}y^{2}+24x^{2}y^{2}}{-12x^{2}y^{2}}$
\item $\dfrac{2a^{4}b^{6}c-4a^{5}b^{3}c^{2}+5a^{3}b^{3}c^{3}}{2a^{2}b^{3}c}$
\item $19x^{2}-10x^{3}+x^{5}-14x+6)\div (x^{2}+1-2x)$
\item $(2x^{3}-31x+35-x^{2})\div (2x-7)$
\item $(2-x^{5})\div (x^{2}+1)$
\item $(3x-5x^{2}+9+x^{3})\div (3-x)$
\item $(2x+3)^{2}-(2x-3)^{2}$
\item $(3x+1)(x+4)-(x+2)^{2}$
\item $(7x^{2}-6)(x+1)+(3x-4)^{3}$
\item $-5(a-b^{2})^{2}+(3a+b)^{3}$
\item $(2x^{2}-3)(3x^{2}-5)-(5x^{2}+6)^{2}$
\item $3x(x-2)+(3x-1)(x+5)-(3-x)^{3}$
\item $\left( 7a+1\right) \left( 7a-1\right) -\left( 4a+1\right)^{3}+2a^{2}\left( 
a-\dfrac{1}{4}\right) ^{2}$
\end{enumerate}

\begin{respuesta}
\begin{multicols}{2}
\begin{enumerate}
\item[1.] $3x^{3}-11x^{2}-11x+17$
\item[3.] $x^{3}-8y^{3}$
\item[5.] $3x^{5}-8x^{4}+12x^{3}-8x^{2}+x+2$
\item[7.] $-2a^{3}c+a^{3}b^{3}+\frac{5}{2}ac^{2}$
\item[9.] $x^{2}+3x+5$
\item[11.] $-x^{2}+2x+3$ 
\item[13.] $2x^{2}+9x$
\item[17.] $x^{3}-3x^{2}+35x-32$
\end{enumerate}
\end{multicols}
\end{respuesta}
\end{ejer}

\section{Operaciones con otros objetos}
bla bla bla blabla blabla blabla blabla blabla blabla blabla blabla blabla blabla blabla 
bla bla bla blabla blabla blabla blabla blabla blabla blabla blabla blabla blabla blabla 
bla bla bla blabla blabla blabla blabla blabla blabla blabla blabla blabla blabla blabla 
bla bla bla blabla blabla blabla blabla blabla blabla blabla blabla blabla blabla blabla 

\seccionDeEjercicios
\begin{ejer}
Efectúe las operaciones indicadas. Exprese el resultado como un
polinomio reducido.
\begin{multicols}{2}
\begin{enumerate}
\item $\left( x+\dfrac{1}{2}\right) ^{2}$
\item $\left( 3-2x\right) ^{2}$
\item $\left( x-\dfrac{2}{3}\right) ^{3}$
\item $\left( 2-x\right) ^{3}$
\item $\left( 2x^{2}-\dfrac{1}{2}+x^{2}\right) ^{2}$
\item $\left( -x-y\right) ^{2}$
\item $\left( -x-y\right) ^{3}$
\item $\left( -x-2y-4x\right) ^{3}$
\item $-\left( 2x^{3}-3t^{3}\right) ^{2}$
\item $\left(-2+x^{2}-3c-x^{2}\right) ^{2}$
\item $\left( \dfrac{x+2u^{2}}{3}\right) ^{2}$
\item $-\left( \dfrac{x^{2}-u^{2}}{2}\right) ^{2}$
\item $\left( \left( x-r\right)^{2}-r^{2}\right) ^{2}$
\item $3\left( x-2t\right) ^{4}-3\left(2t-x\right) ^{4}$
\end{enumerate}
\end{multicols}

\begin{respuesta}
\begin{multicols}{2}
\begin{enumerate}
\item $x^{2}+x+\dfrac{1}{4}$ 
\item $4x^{2}-12x+9$ 
\item $ x^{3}-2x^{2}+\dfrac{4}{3}x-\dfrac{8}{27}$
\item $-x^{3}+6x^{2}-12x+8$
\item $ 9x^{4}-3x^{2}+\dfrac{1}{4}$
\item $ x^{2}+2xy+y^{2}$
\item $-x^{3}-3x^{2}y-3xy^{2}-y^{3}$
\item $-125x^{3}-150x^{2}y-60xy^{2}-8y^{3}$
\item $-9t^{6}+12t^{3}x^{3}-4x^{6}$
\item $9c^{2}+12c+4$
\item $\dfrac{4}{9}u^{4}+\dfrac{4}{9}u^{2}x+\dfrac{1}{9}x^{2}$
\item $-\dfrac{1}{4}u^{4}+\dfrac{1}{2}u^{2}x^{2}-\dfrac{1}{4}x^{4}$
\item $4r^{2}x^{2}-4rx^{3}+x^{4}$
\end{enumerate}
\end{multicols}
\end{respuesta}
\end{ejer}


\begin{ejer}
Determine el cociente y el residuo en cada caso.

\begin{enumerate}
\item $\left( 2x^{3}-x^{2}+2x-1\right) \div \left( x-2\right) $
\item $\left( 4x^{3}+2x^{2}-3x-5\right) \div \left( 2x-1\right) $
\item $\left( x^{8}+x^{6}+x^{4}-x^{2}+x\right) \div \left( x-3\right) $
\item $\left( x^{4}-x^{3}-x^{2}+x^{3}+1\right) \div \left( -x+1\right) $
\item $\left( x^{3}+x^{6}+2x^{5}-\dfrac{x^{2}}{2}+x\right) \div \left(x-1\right) $
\end{enumerate}

\begin{respuesta}
\begin{multicols}{2}
\begin{enumerate}
\item[1.] $3x^{3}-11x^{2}-11x+17$
\item[3.] $x^{3}-8y^{3}$
\item[5.] $3x^{5}-8x^{4}+12x^{3}-8x^{2}+x+2$
\item[7.] $-2a^{3}c+a^{3}b^{3}+\frac{5}{2}ac^{2}$
\item[9.] $x^{2}+3x+5$
\item[11.] $-x^{2}+2x+3$ 
\item[13.] $2x^{2}+9x$
\item[17.] $x^{3}-3x^{2}+35x-32$
\end{enumerate}
\end{multicols}
\end{respuesta}
\end{ejer}

\newpage

\begin{ejer}
Efectúe las operaciones indicadas. Exprese el resultado como un
polinomio reducido.

\begin{enumerate}
\item $-(7x^{2}+3x-4)+(8-x^{2}+5x^{3})-(2x^{3}+3x^{2}-5+8x)$
\item $\left( 11x^{3}-x+7\right) -\left( 2x-4x^{3}-6\right) +\left(7x^{2}-9x+4\right) $
\item $\left( x^{2}+2xy+4y^{2}\right) \left( x-2y\right) $
\item $5a^{3}b^{2}\left( ab^{2}-b+4a\right) -(8a^{3}b^{3}-10a^{4}b^{4})$
\item $(3x^{2}-8x+7)(x^{3}+x)+(2x^{3}-6x+2)$
\item $\dfrac{-36x^{2}y^{2}+24x^{2}y^{2}}{-12x^{2}y^{2}}$
\item $\dfrac{2a^{4}b^{6}c-4a^{5}b^{3}c^{2}+5a^{3}b^{3}c^{3}}{2a^{2}b^{3}c}$
\item $19x^{2}-10x^{3}+x^{5}-14x+6)\div (x^{2}+1-2x)$
\item $(2x^{3}-31x+35-x^{2})\div (2x-7)$
\item $(2-x^{5})\div (x^{2}+1)$
\item $(3x-5x^{2}+9+x^{3})\div (3-x)$
\item $(2x+3)^{2}-(2x-3)^{2}$
\item $(3x+1)(x+4)-(x+2)^{2}$
\item $(7x^{2}-6)(x+1)+(3x-4)^{3}$
\item $-5(a-b^{2})^{2}+(3a+b)^{3}$
\item $(2x^{2}-3)(3x^{2}-5)-(5x^{2}+6)^{2}$
\item $3x(x-2)+(3x-1)(x+5)-(3-x)^{3}$
\item $\left( 7a+1\right) \left( 7a-1\right) -\left( 4a+1\right)^{3}+2a^{2}\left( 
a-\dfrac{1}{4}\right) ^{2}$
\end{enumerate}
\end{ejer}

\Closesolutionfile{solucionario}

\input{solucionario}
\end{document}

An image of the "Respuestas" ("Answers") section showing the desired result:

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