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% Document Info
\author{Mon. (Monz gomz)}
\pdfinfo{
  /Title (algebra-factorizacion.pdf)
  /Creator (Cheatography)
  /Author (Mon. (Monz gomz))
  /Subject (Álgebra - Factorización Cheat Sheet)
}

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\noindent
\begin{multicols}{3}
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    {\parbox{\dimexpr\textwidth-2\fboxsep\relax}{\noindent
        \hspace*{-6pt}\includegraphics[width=5.8cm]{/web/www.cheatography.com/public/images/cheatography_logo.pdf}}
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\begin{tabulary}{11cm}{L}
    \vspace{-2pt}\large{\bf{\textcolor{DarkBackground}{\textrm{Álgebra - Factorización Cheat Sheet}}}} \\
    \normalsize{by \textcolor{DarkBackground}{Mon. (Monz gomz)} via \textcolor{DarkBackground}{\uline{cheatography.com/64672/cs/24031/}}}
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\noindent
\begin{multicols}{3}
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  \mymulticolumn{2}{p{5.377cm}}{\bf\textcolor{white}{Cheatographer}}  \\
  \vspace{-2pt}Mon. (Monz gomz) \\
  \uline{cheatography.com/monz-gomz} \\
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  \mymulticolumn{1}{p{5.377cm}}{\bf\textcolor{white}{Cheat Sheet}}  \\
   \vspace{-2pt}Published 19th August, 2020.\\
   Updated 19th August, 2020.\\
   Page {\thepage} of \pageref{LastPage}.
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  Measure your website readability!\\
  www.readability-score.com
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\begin{document}
\raggedright
\raggedcolumns

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\begin{multicols*}{3}

\begin{tabularx}{5.377cm}{x{2.78712 cm} x{2.18988 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Términos racionales e irracionales}}  \tn
% Row 0
\SetRowColor{LightBackground}
Término racional & No tiene raíz. \tn 
% Row Count 1 (+ 1)
% Row 1
\SetRowColor{white}
Término irracional & Tiene raíz. \tn 
% Row Count 2 (+ 1)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
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\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{x{1.84149 cm} x{3.13551 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Leyes importantes}}  \tn
% Row 0
\SetRowColor{LightBackground}
Ley asociativa & {\bf{abcd= (ab)·(cd)=(abc)·d}} \tn 
% Row Count 2 (+ 2)
% Row 1
\SetRowColor{white}
Ley de signos & {\bf{+·+ = +}} \tn 
% Row Count 3 (+ 1)
% Row 2
\SetRowColor{LightBackground}
Ley de signos & {\bf{- · - = +}} \tn 
% Row Count 4 (+ 1)
% Row 3
\SetRowColor{white}
Ley de signos & {\bf{+ · - = -}} \tn 
% Row Count 5 (+ 1)
% Row 4
\SetRowColor{LightBackground}
Ley de signos & {\bf{- · + = -}} \tn 
% Row Count 6 (+ 1)
% Row 5
\SetRowColor{white}
Ley de signos & {\bf{+ / - = -}} \tn 
% Row Count 7 (+ 1)
% Row 6
\SetRowColor{LightBackground}
Ley de signos & {\bf{+ / + = +}} \tn 
% Row Count 8 (+ 1)
% Row 7
\SetRowColor{white}
Ley de signos & {\bf{- / + = -}} \tn 
% Row Count 9 (+ 1)
% Row 8
\SetRowColor{LightBackground}
Ley de signos & {\bf{- / - = +}} \tn 
% Row Count 10 (+ 1)
% Row 9
\SetRowColor{white}
Ley de exponentes & {\bf{a\textasciicircum{}n\textasciicircum{}· a \textasciicircum{}m\textasciicircum{}= a \textasciicircum{}n+m\textasciicircum{}}} \tn 
% Row Count 12 (+ 2)
% Row 10
\SetRowColor{LightBackground}
Ley de exponentes & {\bf{(a\textasciicircum{}n\textasciicircum{})\textasciicircum{}m\textasciicircum{}= a \textasciicircum{}n·m\textasciicircum{}}} \tn 
% Row Count 14 (+ 2)
% Row 11
\SetRowColor{white}
Ley de exponentes & {\bf{a\textasciicircum{}n\textasciicircum{}/ a \textasciicircum{}m\textasciicircum{}= a \textasciicircum{}n-m\textasciicircum{}}} \tn 
% Row Count 16 (+ 2)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
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\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Productos Notables}}  \tn
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{Ciertos productos que cumplen reglas fijas y el resultado puede ser por inspección.% Row Count 2 (+ 2)
} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Cambios de signos en multiplicación}}  \tn
% Row 0
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\mymulticolumn{1}{x{5.377cm}}{\{\{ac\}\}{\bf{(a-b)(c-d) = -(b-a)(c-d)}}} \tn 
% Row Count 1 (+ 1)
% Row 1
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{\{\{ac\}\}{\bf{(a-b)(c-d) = - (a-b)(d-c)}}} \tn 
% Row Count 2 (+ 1)
% Row 2
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\mymulticolumn{1}{x{5.377cm}}{\{\{ac\}\}{\bf{(a-b)(c-d) = (b-a)(d-c)}}} \tn 
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\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Teorema del residuo}}  \tn
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{Dividir un polinomio entre un binomio de la forma {\bf{x - a}} se obtiene sustituyendo {\bf{x}} por la {\bf{a}}. \newline % Row Count 3 (+ 3)
Cuando el divisor sea de la forma {\bf{bx - a}} donde {\bf{b}} es el coeficiente de {\bf{x}} y distinto a 1, es el residuo obtiene sustituyendo {\bf{x}} por {\bf{a / b}} o cuando sea {\bf{ bx + a}} por {\bf{ - a / b}}% Row Count 7 (+ 4)
} \tn 
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\begin{tabularx}{5.377cm}{X}
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\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Fracciones Heterogéneas}}  \tn
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\mymulticolumn{1}{p{5.377cm}}{\vspace{1px}\centerline{\includegraphics[width=5.1cm]{/web/www.cheatography.com/public/uploads/monz-gomz_1597636870_Ilustración_sin_título.jpg}}} \tn 
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\begin{tabularx}{5.377cm}{X}
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\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Conjugación}}  \tn
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\mymulticolumn{1}{x{5.377cm}}{El mismo término con signo opuesto} \tn 
% Row Count 1 (+ 1)
% Row 1
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\mymulticolumn{1}{x{5.377cm}}{(a + b){\bf{(a - b)}} = a\textasciicircum{}2\textasciicircum{}- b\textasciicircum{}2\textasciicircum{}} \tn 
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% Row 2
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{Raíz(4 + x) - 2 -{}-{}-\textgreater{} {\bf{conjugado es}} Raíz(4 + x) + 2} \tn 
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\begin{tabularx}{5.377cm}{X}
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\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Division sintética}}  \tn
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{Permite hallar el {\bf{cociente y residuo}} de una división de polinomio y binomio.% Row Count 2 (+ 2)
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\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{División sintética}}  \tn
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\mymulticolumn{1}{p{5.377cm}}{\vspace{1px}\centerline{\includegraphics[width=5.1cm]{/web/www.cheatography.com/public/uploads/monz-gomz_1597804385_Ilustración_sin_título 6.jpg}}} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
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\begin{tabularx}{5.377cm}{X}
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\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Es divisible solo si...}}  \tn
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\mymulticolumn{1}{p{5.377cm}}{\vspace{1px}\centerline{\includegraphics[width=5.1cm]{/web/www.cheatography.com/public/uploads/monz-gomz_1597636791_IMG_0083.JPG}}} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
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\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Racionalización}}  \tn
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{Se multiplica ambos términos por algo que haga al denominador raíz exacta. \newline % Row Count 2 (+ 2)
- Se multiplica por la conjugada del denominador. \newline % Row Count 3 (+ 1)
- Si son 3 radicales se multiplica por la conjugada del denominador y luego por la conjugada del resultado.% Row Count 6 (+ 3)
} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
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\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Radicales}}  \tn
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\mymulticolumn{1}{p{5.377cm}}{\vspace{1px}\centerline{\includegraphics[width=5.1cm]{/web/www.cheatography.com/public/uploads/monz-gomz_1597637338_Ilustración_sin_título 2.jpg}}} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
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\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Radicales}}  \tn
\SetRowColor{LightBackground}
\mymulticolumn{1}{p{5.377cm}}{\vspace{1px}\centerline{\includegraphics[width=5.1cm]{/web/www.cheatography.com/public/uploads/monz-gomz_1597637393_Ilustración_sin_título 3.jpg}}} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{x{2.28942 cm} x{2.68758 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{{\bf{Factores}}}}  \tn
% Row 0
\SetRowColor{LightBackground}
Factor común & {\bf{10b - 30ab\textasciicircum{}2\textasciicircum{} = 10b(1 - 3ab)}} \tn 
% Row Count 2 (+ 2)
% Row 1
\SetRowColor{white}
Agrupación de términos & {\bf{ax+bx+ay+by = (a+b)(x+y)}} \tn 
% Row Count 4 (+ 2)
% Row 2
\SetRowColor{LightBackground}
Trinomio Cuadrado Perfecto & {\bf{m\textasciicircum{}2\textasciicircum{}+ 2m + 1 = (m+1)\textasciicircum{}2\textasciicircum{}}} \tn 
% Row Count 6 (+ 2)
% Row 3
\SetRowColor{white}
Diferencia de Cuadrados Perfectos & {\bf{16x\textasciicircum{}2\textasciicircum{}-25y\textasciicircum{}4\textasciicircum{}= (4x+5y\textasciicircum{}2\textasciicircum{})(4x-5y\textasciicircum{}2\textasciicircum{})}} \tn 
% Row Count 8 (+ 2)
% Row 4
\SetRowColor{LightBackground}
Trinomio de la forma {\bf{x\textasciicircum{}2\textasciicircum{}+bx+c}} & {\bf{x\textasciicircum{}2\textasciicircum{}+5x+6 = (x+2)(x+3)}} {\emph{sumados 5, producto 6}} \tn 
% Row Count 11 (+ 3)
% Row 5
\SetRowColor{white}
Suma de cubos perfectos & {\bf{a\textasciicircum{}3\textasciicircum{}+b\textasciicircum{}3\textasciicircum{}= (a+b)(a\textasciicircum{}2\textasciicircum{}-ab+b\textasciicircum{}2\textasciicircum{})}} \tn 
% Row Count 13 (+ 2)
% Row 6
\SetRowColor{LightBackground}
Diferencia de cubos & {\bf{a\textasciicircum{}3\textasciicircum{}-b\textasciicircum{}3\textasciicircum{}= (a-b)(a\textasciicircum{}2\textasciicircum{}+ab+b\textasciicircum{}2\textasciicircum{})}} \tn 
% Row Count 15 (+ 2)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\SetRowColor{LightBackground}
\mymulticolumn{2}{x{5.377cm}}{- {\emph{Al multiplicar los factores debe dar la expresión original.}} \newline Trinomio Cuadrado Perfecto también llamado TCP}  \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
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\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Factores. TCP por adición o Sustracción}}  \tn
\SetRowColor{LightBackground}
\mymulticolumn{1}{p{5.377cm}}{\vspace{1px}\centerline{\includegraphics[width=5.1cm]{/web/www.cheatography.com/public/uploads/monz-gomz_1597803092_Ilustración_sin_título 4.jpg}}} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Factores. Trinomio de la forma ax\textasciicircum{}2\textasciicircum{}+ bx + c}}  \tn
\SetRowColor{LightBackground}
\mymulticolumn{1}{p{5.377cm}}{\vspace{1px}\centerline{\includegraphics[width=5.1cm]{/web/www.cheatography.com/public/uploads/monz-gomz_1597803625_Ilustración_sin_título 5.jpg}}} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
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\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Factores. Cubo perfecto de binomio}}  \tn
\SetRowColor{LightBackground}
\mymulticolumn{1}{p{5.377cm}}{\vspace{1px}\centerline{\includegraphics[width=5.1cm]{/web/www.cheatography.com/public/uploads/monz-gomz_1597806034_Ilustración_sin_título 8.jpg}}} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
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\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Factores. Suma o diferencia de potencias}}  \tn
% Row 0
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{Teorema del residuo} \tn 
% Row Count 1 (+ 1)
% Row 1
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{Diferencia de {\emph{potencias iguales}}, es divisible entre la {\bf{diferencia, sean pares o impares.}}} \tn 
% Row Count 3 (+ 2)
% Row 2
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{Diferencia de {\emph{potencias iguales}} pares es divisible {\bf{por la suma}}} \tn 
% Row Count 5 (+ 2)
% Row 3
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{{\emph{Sumatoria de potencias iguales impares}}, es divisible por {\bf{la suma.}}} \tn 
% Row Count 7 (+ 2)
% Row 4
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{{\emph{Sumatoria de potencias iguales pares}}, {\bf{no es divisible.}}} \tn 
% Row Count 9 (+ 2)
\hhline{>{\arrayrulecolor{DarkBackground}}-}
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\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
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\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Ejemplo.}}  \tn
\SetRowColor{LightBackground}
\mymulticolumn{1}{p{5.377cm}}{\vspace{1px}\centerline{\includegraphics[width=5.1cm]{/web/www.cheatography.com/public/uploads/monz-gomz_1597805699_Ilustración_sin_título 7.jpg}}} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}


% That's all folks
\end{multicols*}

\end{document}