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%TCIDATA{<META NAME="Title" CONTENT="Simplify">}
%TCIDATA{Created=Mon Aug 19 14:52:24 1996}
%TCIDATA{LastRevised=Thu Feb 13 21:45:11 1997}
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\input{tcilatex}
\begin{document}


\subsection{Simplify\label{Simplify}\hrulefill}

You can reduce expressions to standard form, collecting like terms in
addition and canceling common factors in division. When possible, Maple
performs indicated operations exactly or reduces them to lower-level
operations.

\subparagraph{\FRAME{itbpF}{50.75pt}{21.75pt}{6pt}{}{}{ex3.wmf}{\special%
{language "Scientific Word";type "GRAPHIC";display "PICT";valid-file
"F";width 50.75pt;height 21.75pt;depth 6pt;original-width
48.875pt;original-height 19.5625pt;cropleft "0";croptop "1";cropright
"1";cropbottom "0";filename 'ex3.WMF';file-properties "XNPEU";}}Simplify $%
4a+7b-\left( 2a+b\right) $}

\begin{enumerate}
\item  Click\FRAME{itbpF}{20.125pt}{20.125pt}{2pt}{}{}{text.wmf}{\special%
{language "Scientific Word";type "GRAPHIC";maintain-aspect-ratio
TRUE;display "PICT";valid_file "F";width 20.125pt;height 20.125pt;depth
2pt;original-width 16.0625pt;original-height 16.0625pt;cropleft "0";croptop
"1";cropright "1";cropbottom "0";filename 'text.wmf';file-properties
"XNPEU";}}or, from the Insert menu, choose Math to start mathematics.

\item  Type \textbf{4a+7b-}, click\FRAME{itbpF}{19.8125pt}{18.9375pt}{2pt}{}{%
}{parens.wmf}{\special{language "Scientific Word";type
"GRAPHIC";maintain-aspect-ratio TRUE;display "PICT";valid_file "F";width
19.8125pt;height 18.9375pt;depth 2pt;original-width
17.8125pt;original-height 16.9375pt;cropleft "0";croptop "1";cropright
"1";cropbottom "0";filename 'parens.wmf';file-properties "XNPEU";}}, and
type \textbf{2a+b}, click\FRAME{itbpF}{23.0625pt}{22pt}{2pt}{}{}{simplify.wmf%
}{\special{language "Scientific Word";type "GRAPHIC";maintain-aspect-ratio
TRUE;display "PICT";valid_file "F";width 23.0625pt;height 22pt;depth
2pt;original-width 17.8125pt;original-height 16.9375pt;cropleft "0";croptop
"1";cropright "1";cropbottom "0";filename 'simplify.wmf';file-properties
"XNPEU";}}or, from the Maple menu, choose Simplify. Maple returns this
answer: \ $2a+6b.$\medskip 
\end{enumerate}

\subparagraph{\FRAME{itbpF}{50.75pt}{21.75pt}{6pt}{}{}{ex3.wmf}{\special%
{language "Scientific Word";type "GRAPHIC";display "PICT";valid-file
"F";width 50.75pt;height 21.75pt;depth 6pt;original-width
48.875pt;original-height 19.5625pt;cropleft "0";croptop "1";cropright
"1";cropbottom "0";filename 'ex3.WMF';file-properties "XNPEU";}}Simplify $%
\left( x^{2}-6x+\left( \frac{-6}{2}\right) ^{2}\right) +\left(
y^{2}+10y\left( \frac{10}{2}\right) ^{2}\right) $}

\begin{enumerate}
\item  Enter the first expression:

\begin{enumerate}
\item  Click\FRAME{itbpF}{19.8125pt}{18.9375pt}{2pt}{}{}{parens.wmf}{\special%
{language "Scientific Word";type "GRAPHIC";maintain-aspect-ratio
TRUE;display "PICT";valid_file "F";width 19.8125pt;height 18.9375pt;depth
2pt;original-width 17.8125pt;original-height 16.9375pt;cropleft "0";croptop
"1";cropright "1";cropbottom "0";filename 'parens.wmf';file-properties
"XNPEU";}}or, from the Insert menu, choose Brackets and choose OK.

\item  Type \textbf{x}, click\FRAME{itbpF}{19.5625pt}{18.8125pt}{2pt}{}{}{%
supscrip.wmf}{\special{language "Scientific Word";type "GRAPHIC";display
"PICT";valid_file "F";width 19.5625pt;height 18.8125pt;depth
2pt;original-width 17.8125pt;original-height 16.9375pt;cropleft "0";croptop
"1";cropright "1";cropbottom "0";filename 'supscrip.wmf';file-properties
"XNPEU";}}or, from \ the Insert menu, choose Superscript.

\item  Type \textbf{2},\textbf{\ }and press spacebar.

\item  Type -\textbf{6x+}, click\FRAME{itbpF}{19.8125pt}{18.9375pt}{2pt}{}{}{%
parens.wmf}{\special{language "Scientific Word";type
"GRAPHIC";maintain-aspect-ratio TRUE;display "PICT";valid_file "F";width
19.8125pt;height 18.9375pt;depth 2pt;original-width
17.8125pt;original-height 16.9375pt;cropleft "0";croptop "1";cropright
"1";cropbottom "0";filename 'parens.wmf';file-properties "XNPEU";}}, and
then click\FRAME{itbpF}{19.5625pt}{18.8125pt}{2pt}{}{}{fraction.wmf}{\special%
{language "Scientific Word";type "GRAPHIC";display "PICT";valid_file
"F";width 19.5625pt;height 18.8125pt;depth 2pt;original-width
17.8125pt;original-height 16.9375pt;cropleft "0";croptop "1";cropright
"1";cropbottom "0";filename 'fraction.wmf';file-properties "XNPEU";}}or,
from the Insert menu, choose Fraction.

\item  Type \textbf{-6, }press Tab, type \textbf{2},\textbf{\ }and press
spacebar twice.

\item  Click\FRAME{itbpF}{19.5625pt}{18.8125pt}{2pt}{}{}{supscrip.wmf}{%
\special{language "Scientific Word";type "GRAPHIC";display "PICT";valid_file
"F";width 19.5625pt;height 18.8125pt;depth 2pt;original-width
17.8125pt;original-height 16.9375pt;cropleft "0";croptop "1";cropright
"1";cropbottom "0";filename 'supscrip.wmf';file-properties "XNPEU";}}, type 
\textbf{2},\textbf{\ }and press spacebar twice.
\end{enumerate}

\item  Type the second expression:

\begin{enumerate}
\item  Type \textbf{+ }, click\FRAME{itbpF}{19.8125pt}{18.9375pt}{2pt}{}{}{%
parens.wmf}{\special{language "Scientific Word";type
"GRAPHIC";maintain-aspect-ratio TRUE;display "PICT";valid_file "F";width
19.8125pt;height 18.9375pt;depth 2pt;original-width
17.8125pt;original-height 16.9375pt;cropleft "0";croptop "1";cropright
"1";cropbottom "0";filename 'parens.wmf';file-properties "XNPEU";}}, type 
\textbf{y}, click\FRAME{itbpF}{19.5625pt}{18.8125pt}{2pt}{}{}{supscrip.wmf}{%
\special{language "Scientific Word";type "GRAPHIC";display "PICT";valid_file
"F";width 19.5625pt;height 18.8125pt;depth 2pt;original-width
17.8125pt;original-height 16.9375pt;cropleft "0";croptop "1";cropright
"1";cropbottom "0";filename 'supscrip.wmf';file-properties "XNPEU";}}, type 
\textbf{2},\textbf{\ }and press spacebar.

\item  Type \textbf{+10y}, click\FRAME{itbpF}{19.8125pt}{18.9375pt}{2pt}{}{}{%
parens.wmf}{\special{language "Scientific Word";type
"GRAPHIC";maintain-aspect-ratio TRUE;display "PICT";valid_file "F";width
19.8125pt;height 18.9375pt;depth 2pt;original-width
17.8125pt;original-height 16.9375pt;cropleft "0";croptop "1";cropright
"1";cropbottom "0";filename 'parens.wmf';file-properties "XNPEU";}}, and
then click\FRAME{itbpF}{19.5625pt}{18.8125pt}{2pt}{}{}{fraction.wmf}{\special%
{language "Scientific Word";type "GRAPHIC";display "PICT";valid_file
"F";width 19.5625pt;height 18.8125pt;depth 2pt;original-width
17.8125pt;original-height 16.9375pt;cropleft "0";croptop "1";cropright
"1";cropbottom "0";filename 'fraction.wmf';file-properties "XNPEU";}}.

\item  Type \textbf{10, }press Tab, type \textbf{2}, press spacebar twice,
click\FRAME{itbpF}{19.5625pt}{18.8125pt}{2pt}{}{}{supscrip.wmf}{\special%
{language "Scientific Word";type "GRAPHIC";display "PICT";valid_file
"F";width 19.5625pt;height 18.8125pt;depth 2pt;original-width
17.8125pt;original-height 16.9375pt;cropleft "0";croptop "1";cropright
"1";cropbottom "0";filename 'supscrip.wmf';file-properties "XNPEU";}}, and
type \textbf{2}.
\end{enumerate}

\item  Click\FRAME{itbpF}{22.4375pt}{21.0625pt}{2pt}{}{}{simplify.wmf}{%
\special{language "Scientific Word";type "GRAPHIC";display "PICT";valid_file
"F";width 22.4375pt;height 21.0625pt;depth 2pt;original-width
17.8125pt;original-height 16.9375pt;cropleft "0";croptop "1";cropright
"1";cropbottom "0";filename 'simplify.wmf';file-properties "XNPEU";}}or,
from the Maple menu, choose Simplify. Maple simplifies the mathematics:
\end{enumerate}

\begin{center}
$\left( x^{2}-6x+\left( \frac{-6}{2}\right) ^{2}\right) +\left(
y^{2}+10y\left( \frac{10}{2}\right) ^{2}\right) =\allowbreak
x^{2}-6x+9+y^{2}+250y$\medskip
\end{center}

\subparagraph{\textit{Simplify these expressions\label{exercises}\protect%
\medskip }}

\begin{quotation}
\[
\rule[-0.05in]{0in}{0.3in}\sqrt[3]{8}+3\text{\hspace{0.5in}}\sin ^{2}x+\cos
^{2}x\text{\hspace{0.5in}}\dint_{1}^{a}\dfrac{1}{t}dt\text{\hspace{0.5in}}14%
\dfrac{5}{9}\text{\hspace{0.5in}}\dfrac{3x^{2}+3x}{8x^{2}+7}+\dfrac{5x^{2}+3%
}{2x^{2}+x+7} 
\]
\end{quotation}

\end{document}
