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

answers

I'm writing a book and for it I have created a little class file.

Each section in the book have (sub-)section of exercises. At the end of all the chapters I want to put a chapter* of answers to some of the exercises. Since the exercises are numbered by section (i.e. the exercise's counter reset whenever the section step), I want to group the answers according to the section (and the chapter) of the exercise they answer to. What I want is something like this:

mwe

Here is the relevant code of the class file.
The commented lines are my unsuccessful attempts to achieve what I want. I have leaved almost all the packages to see if there some compatibility problem.

\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}

\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}

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

%\let\c@hapter\chapter
%\renewcommand{\chapter}{
%   \c@hapter
%   \Writetofile{solucionario}{\protect\paragraph*{Capítulo \Roman{\thechapter}.\space 
%   \leftmark}}
%}

\newcommand{\seccionDeEjercicios}{%
  \newpage%
  \kern 5mm
  \hrule
  \kern 3mm
  \null \hfill {\large Ejercicios~\thesection.~\rightmark}\par
  \kern 3mm
  \hrule
  \kern 5mm
  \Writetofile{solucionario}{\protect\paragraph*{Ejercicios\space\thesection.
  \space\rightmark}}
  }

\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}}

\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}}
%   \begin{Filesave}{solucionario}
%   \protect\chapter*{Respuestas}
%   \protect\fancyhf{}
%   \protect\fancyhead[LO]{\small\textsl{Soluciones a los ejercicios}}          
%   \protect\fancyhead[RE]{\small\textsl{Soluciones a los ejercicios}}           
%   \protect\fancyhead[LE,RO]{\thepage}                         
%   \end{Filesave}
}

The \seccionDeEjercicios command was provided by this answer.

Here is an example of my document:

\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 

\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}

\Closesolutionfile{solucionario}

\input{solucionario}
\end{document}

Edit: Here the relevant code of my class, with chapters based on fncychap (as requested). Some code to differentiate the style of the chapters, was provided by egreg in this.

\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[Sonny]{fncychap}
\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}

% Chapters
\ChNameVar{\bf\LARGE}               
\ChNumVar{\LARGE}                   
\ChTitleVar{\LARGE\normalfont}      
\ChRuleWidth{0.5pt}                 
\ChNameAsIs                         
\ChTitleAsIs                        
\renewcommand{\DOCH}{}
\renewcommand{\DOTI}[1]{%
    \vspace*{-0.9cm}
    \CTV\raggedleft\mghrulefill{\RW}\par\nobreak
    \vskip 2\p@
    \CNV\FmN{\@chapapp}\space\CNoV\Roman{chapter}.\space\CTV\FmTi{#1}\par\nobreak
    \vspace*{-11\p@}
    \mghrulefill{\RW}\par\nobreak
    \vspace*{40\p@}}
\renewcommand{\DOTIS}[1]{%
    \vspace*{-9mm}
    \CTV\raggedleft
    \CTV\FmTi{#1}\par\nobreak
    \vspace*{-11\p@}
    \mghrulefill{\RW}\par\nobreak
    \vspace*{40\p@}}


\renewcommand\@seccntformat[1]{
    {\csname the#1\endcsname}.\hspace{0.5em}}
\renewcommand\section{\@startsection
    {section}{1}{0mm}               
    {6pt}                           
    {1pt}                           
    {\bfseries}}                    

\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}


\let\c@hapter\chapter
\renewcommand{\chapter}{
  \ifnum\value{chapter}>0 
    \cambiarseccionydefi 
    \let\chapter\c@hapter
  \fi
    \c@hapter
}
\def\cambiarseccionydefi{%
   \renewcommand\section{\@startsection{section}{1}{0mm}{6pt}{1pt}{\Large}}%
   \@addtoreset{definicion}{section}%
   \renewcommand{\thedefi}{\thesection.\arabic{definicion}}%
 }

\newcommand{\seccionDeEjercicios}{%
  \newpage%
  \kern 5mm
  \hrule
  \kern 3mm
  \null \hfill {\large Ejercicios~\thesection.~\rightmark}\par
  \kern 3mm
  \hrule
  \kern 5mm
}


\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}}
}

Best Answer

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:

enter image description here

Related Question