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% Document Info
\author{Khionne (khionne)}
\pdfinfo{
  /Title (college-and-advanced-algebra-1st.pdf)
  /Creator (Cheatography)
  /Author (Khionne (khionne))
  /Subject (College and Advanced Algebra –1st Cheat Sheet)
}

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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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    \vspace{-2pt}\large{\bf{\textcolor{DarkBackground}{\textrm{College and Advanced Algebra –1st Cheat Sheet}}}} \\
    \normalsize{by \textcolor{DarkBackground}{Khionne (khionne)} via \textcolor{DarkBackground}{\uline{cheatography.com/193579/cs/40286/}}}
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  \mymulticolumn{2}{p{5.377cm}}{\bf\textcolor{white}{Cheatographer}}  \\
  \vspace{-2pt}Khionne (khionne) \\
  \uline{cheatography.com/khionne} \\
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  \mymulticolumn{1}{p{5.377cm}}{\bf\textcolor{white}{Cheat Sheet}}  \\
   \vspace{-2pt}Not Yet Published.\\
   Updated 13th September, 2023.\\
   Page {\thepage} of \pageref{LastPage}.
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  Measure your website readability!\\
  www.readability-score.com
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\begin{multicols*}{4}

\begin{tabularx}{3.833cm}{X}
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\mymulticolumn{1}{x{3.833cm}}{\bf\textcolor{white}{Order of Operations}}  \tn
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\mymulticolumn{1}{x{3.833cm}}{BODMAS / PEMDAS} \tn 
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\mymulticolumn{1}{x{3.833cm}}{B - Brackets: Perform operations inside parentheses or brackets first. \newline O - Orders: Evaluate expressions with exponents (powers and roots). \newline D - Division: Perform division from left to right. \newline M - Multiplication: Perform multiplication from left to right. \newline A - Addition: Perform addition from left to right. \newline S - Subtraction: Perform subtraction from left to right.}  \tn 
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\mymulticolumn{1}{x{3.833cm}}{\bf\textcolor{white}{SPECIAL PRODUCTS INVOLVING CUBES}}  \tn
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\mymulticolumn{1}{x{3.833cm}}{The products are just the result of multiplying out the bracket.} \tn 
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\mymulticolumn{1}{x{3.833cm}}{(x + y)3 = x3 + 3x2y + 3xy2 + y3 (Cube of a sum)  \newline (x − y)3 = x3 − 3x2y + 3xy2 − y3 (Cube of a difference)  \newline (x + y)(x2 − xy + y2) = x3 + y3 (Sum of 2 cubes)  \newline (x − y)(x2 + xy + y2) = x3 − y3 (Difference of 2 cubes}  \tn 
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\mymulticolumn{1}{x{3.833cm}}{\bf\textcolor{white}{Law of Inclusion and Exclusion}}  \tn
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\mymulticolumn{1}{x{3.833cm}}{PROBLEM SETS} \tn 
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\mymulticolumn{1}{x{3.833cm}}{For three sets A, B, and C: \newline |A ∪ B ∪ C| = |A| + |B| + |C| - |A ∩ B| - |A ∩ C| - |B ∩ C| + |A ∩ B ∩ C| \newline and  \newline |A ∩ B ∩ C| = |A ∩ B ∩ C| - |A| - |B| - |C| + |A ∩ B| + |A ∩ C| + |B ∩ C|}  \tn 
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\begin{tabularx}{3.833cm}{X}
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\mymulticolumn{1}{x{3.833cm}}{\bf\textcolor{white}{THE FOIL METHOD}}  \tn
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\mymulticolumn{1}{x{3.833cm}}{FOIL – is sometimes used to find the product of two binomials.} \tn 
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\mymulticolumn{1}{x{3.833cm}}{We multiply, \newline • the First terms, \newline • the Outer terms, \newline • the Inner terms, and then \newline • the Last terms of each binomials.}  \tn 
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\mymulticolumn{1}{x{3.833cm}}{\bf\textcolor{white}{Venn Diagram}}  \tn
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\mymulticolumn{1}{x{3.833cm}}{\bf\textcolor{white}{RULES OF EXPONENT}}  \tn
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\mymulticolumn{1}{x{3.833cm}}{Product of a binomial and a trinomial of the form.} \tn 
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\mymulticolumn{1}{x{3.833cm}}{(a + b)(c + d + e) = ac + ad + ae + bc + bd + be \newline  \newline Monomial= 2y$^{\textrm{2}}$, 2 \newline Binomial  = (2y$^{\textrm{2}}$-2) \newline Trinomial = ( 2y$^{\textrm{3}}$+y$^{\textrm{2}}$+2)}  \tn 
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\mymulticolumn{1}{x{3.833cm}}{•Products in algebra have patterns that occur frequently \newline % Row Count 2 (+ 2)
• These patterns are called special products \newline % Row Count 3 (+ 1)
( x + y )$^{\textrm{2}}$ = x$^{\textrm{2}}$ + 2xy + y$^{\textrm{2}}$ (Square of a sum)  \newline % Row Count 4 (+ 1)
( x − y )$^{\textrm{2}}$ = x$^{\textrm{2}}$ − 2xy + y$^{\textrm{2}}$ (Square of a difference)% Row Count 6 (+ 2)
} \tn 
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\mymulticolumn{1}{x{3.833cm}}{(a + b)(a - b) = a2 - b2}  \tn 
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% That's all folks
\end{multicols*}

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