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0 0 0 1 }{CSTYLE "" -1 281 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }
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ing 2" 3 4 1 {CSTYLE "" -1 -1 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }0 
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{SECT 0 {SECT 1 {PARA 256 "" 0 "" {TEXT -1 66 "Chapter 7\n\nManipulati
ons of Polynomials\n and Rational Expressions\n" }}{PARA 0 "" 0 "" 
{TEXT 288 31 "\251 Copyright 2003 by Andr\351 Heck." }}}{SECT 1 {PARA 
0 "" 0 "" {TEXT 257 2 "1." }{TEXT -1 98 " Describe a canonical simplif
ication of univariate rational functions with rational coefficients.\n
" }}{PARA 0 "" 0 "" {TEXT -1 65 "Carry out the following steps to get \+
the expanded canonical form:" }}{PARA 0 "" 0 "" {TEXT -1 28 "(i) conve
rt expression into " }{XPPEDIT 18 0 "numerator / denominator" "6#*&%*n
umeratorG\"\"\"%,denominatorG!\"\"" }{TEXT -1 2 " ;" }}{PARA 0 "" 0 "
" {TEXT -1 31 "(ii) remove common divisors in " }{XPPEDIT 18 0 "numera
tor" "6#%*numeratorG" }{TEXT -1 5 " and " }{XPPEDIT 18 0 "denominator
" "6#%,denominatorG" }{TEXT -1 38 " so that they become relatively pri
me;" }}{PARA 0 "" 0 "" {TEXT -1 18 "(iii) convert the " }{XPPEDIT 18 
0 "numerator" "6#%*numeratorG" }{TEXT -1 5 " and " }{XPPEDIT 18 0 "den
ominator" "6#%,denominatorG" }{TEXT -1 28 " in expanded canonical form
;" }}{PARA 0 "" 0 "" {TEXT -1 36 "(iv) Divide each coefficient in the \+
" }{XPPEDIT 18 0 "denominator" "6#%,denominatorG" }{TEXT -1 5 " and " 
}{XPPEDIT 18 0 "numerator" "6#%*numeratorG" }{TEXT -1 35 " by the lead
ing coefficient of the " }{XPPEDIT 18 0 "denominator" "6#%,denominator
G" }{TEXT -1 6 " (the " }{XPPEDIT 18 0 "denominator" "6#%,denominatorG
" }{TEXT -1 16 " becomes monic)." }}}{SECT 1 {PARA 0 "" 0 "" {TEXT 
258 2 "2." }{TEXT -1 122 " Consider the following rational expression.
\n                                                                    \+
         " }{XPPEDIT 18 0 "(x^4+x^3-4*x^2-4*x)/(x^4+x^3-x^2-x)" "6#*&,
**$%\"xG\"\"%\"\"\"*$F&\"\"$F(*&F'F(*$F&\"\"#F(!\"\"*&F'F(F&F(F.F(,**$
F&F'F(*$F&F*F(*$F&F-F.F&F.F." }{TEXT -1 43 "\nTransform this expressio
n with Maple into\n" }{TEXT 261 3 "(a)" }{TEXT -1 3 "   " }{XPPEDIT 
18 0 "(x^2-4)/(x^2-1)" "6#*&,&*$%\"xG\"\"#\"\"\"\"\"%!\"\"F(,&*$F&F'F(
F(F*F*" }{TEXT -1 2 "\n\n" }{TEXT 262 3 "(b)" }{TEXT -1 3 "   " }
{XPPEDIT 18 0 "(x-2)*(x+2)/(x^2-1)" "6#*(,&%\"xG\"\"\"\"\"#!\"\"F&,&F%
F&F'F&F&,&*$F%F'F&F&F(F(" }{TEXT -1 1 "\n" }}{SECT 1 {PARA 5 "" 0 "" 
{TEXT 263 3 "(a)" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "expr := (x^4+x^3-4*x^2-
4*x)/(x^4+x^3-x^2-x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%exprG*&,**
$)%\"xG\"\"%\"\"\"F+*$)F)\"\"$F+F+*&F*F+)F)\"\"#F+!\"\"*&F*F+F)F+F2F+,
*F'F+F,F+*$F0F+F2F)F2F2" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "
normal(expr);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&,&*$)%\"xG\"\"#\"\"
\"F)\"\"%!\"\"F),&F%F)F)F+F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 0 "" }}}}{SECT 1 {PARA 5 "" 0 "" {TEXT 264 3 "(b)" }}{EXCHG {PARA 0 
"> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 44 "expr := (x^4+x^3-4*x^2-4*x)/(x^4+x^3-x^2-x);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%exprG*&,**$)%\"xG\"\"%\"\"\"F+*$)F)
\"\"$F+F+*&F*F+)F)\"\"#F+!\"\"*&F*F+F)F+F2F+,*F'F+F,F+*$F0F+F2F)F2F2" 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "normal(expr);" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#*&,&*$)%\"xG\"\"#\"\"\"F)\"\"%!\"\"F),&F%F)F
)F+F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "factor(numer(%)) /
 denom(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*(,&%\"xG\"\"\"\"\"#!\"
\"F&,&F%F&F'F&F&,&*$)F%F'F&F&F&F(F(" }}}{PARA 0 "" 0 "" {TEXT -1 17 "I
n one statement:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "applyop(
factor, 1, normal(expr));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*(,&%\"xG
\"\"\"\"\"#!\"\"F&,&F%F&F'F&F&,&*$)F%F'F&F&F&F(F(" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 0 "" }}}}}{SECT 1 {PARA 0 "" 0 "" {TEXT 259 2 "3
." }{TEXT -1 121 " Consider the following rational expression.\n      \+
                                                                      \+
" }{XPPEDIT 18 0 "2*((x^3-y*x^2-y*x+y^2)/(x^3-y*x^2-x+y))" "6#*&\"\"#
\"\"\"*&,**$%\"xG\"\"$F%*&%\"yGF%*$F)F$F%!\"\"*&F,F%F)F%F.*$F,F$F%F%,*
*$F)F*F%*&F,F%*$F)F$F%F.F)F.F,F%F.F%" }{TEXT -1 20 "\nTransform it int
o:\n" }{TEXT 265 3 "(a)" }{TEXT -1 3 "   " }{XPPEDIT 18 0 "2*((x^2-y)/
(x^2-1))" "6#*&\"\"#\"\"\"*&,&*$%\"xGF$F%%\"yG!\"\"F%,&*$F)F$F%F%F+F+F
%" }{TEXT -1 2 "\n\n" }{TEXT 266 3 "(b)" }{TEXT -1 3 "   " }{XPPEDIT 
18 0 "2*((x^2-y)/((x-1)*(x+1))" "6#*&\"\"#\"\"\"*&,&*$%\"xGF$F%%\"yG!
\"\"F%*&,&F)F%F%F+F%,&F)F%F%F%F%F+F%" }{TEXT -1 2 "\n\n" }{TEXT 267 3 
"(c)" }{TEXT -1 3 "   " }{XPPEDIT 18 0 "2-(y-1)/(x-1) + (y-1)/(x+1)" "
6#,(\"\"#\"\"\"*&,&%\"yGF%F%!\"\"F%,&%\"xGF%F%F)F)F)*&,&F(F%F%F)F%,&F+
F%F%F%F)F%" }{TEXT -1 2 "\n\n" }{TEXT 268 3 "(d)" }{TEXT -1 3 "   " }
{XPPEDIT 18 0 "2-2*((y-1)/(x^2-1))" "6#,&\"\"#\"\"\"*&F$F%*&,&%\"yGF%F
%!\"\"F%,&*$%\"xGF$F%F%F*F*F%F*" }{TEXT -1 1 "\n" }}{SECT 1 {PARA 5 "
" 0 "" {TEXT 269 3 "(a)" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "re
start;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "expr := 2*(x^3-y*
x^2-y*x+y^2)/(x^3-y*x^2-x+y);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%ex
prG,$*(\"\"#\"\"\",**$)%\"xG\"\"$F(F(*&%\"yGF()F,F'F(!\"\"*&F/F(F,F(F1
*$)F/F'F(F(F(,*F*F(F.F1F,F1F/F(F1F(" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 13 "normal(expr);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*(
\"\"#\"\"\",&*$)%\"xGF%F&F&%\"yG!\"\"F&,&F(F&F&F,F,F&" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 5 "" 0 "" {TEXT 
270 3 "(b)" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "expr := 2*(x^3-y*x^2-y*x+y^2
)/(x^3-y*x^2-x+y);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%exprG,$*(\"\"
#\"\"\",**$)%\"xG\"\"$F(F(*&%\"yGF()F,F'F(!\"\"*&F/F(F,F(F1*$)F/F'F(F(
F(,*F*F(F.F1F,F1F/F(F1F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 
"factor(expr);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$**\"\"#\"\"\",&*$)
%\"xGF%F&F&%\"yG!\"\"F&,&F*F&F&F,F,,&F*F&F&F&F,F&" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 5 "" 0 "" {TEXT 271 3 "(c
)" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "expr := 2*(x^3-y*x^2-y*x+y^2)/(x^3-
y*x^2-x+y);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%exprG,$*(\"\"#\"\"\"
,**$)%\"xG\"\"$F(F(*&%\"yGF()F,F'F(!\"\"*&F/F(F,F(F1*$)F/F'F(F(F(,*F*F
(F.F1F,F1F/F(F1F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "conver
t(expr, parfrac, x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,(\"\"#\"\"\"*
&,&%\"yG!\"\"F%F%F%,&%\"xGF%F%F)F)F%*&,&F(F%F%F)F%,&F+F%F%F%F)F%" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 5 "" 0 "
" {TEXT 272 3 "(d)" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart
;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "expr := 2*(x^3-y*x^2-y
*x+y^2)/(x^3-y*x^2-x+y);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%exprG,$
*(\"\"#\"\"\",**$)%\"xG\"\"$F(F(*&%\"yGF()F,F'F(!\"\"*&F/F(F,F(F1*$)F/
F'F(F(F(,*F*F(F.F1F,F1F/F(F1F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 26 "convert(expr, parfrac, x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#
,(\"\"#\"\"\"*&,&%\"yG!\"\"F%F%F%,&%\"xGF%F%F)F)F%*&,&F%F)F(F%F%,&F+F%
F%F%F)F%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "2 - normal(2-%,
 expanded);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&\"\"#\"\"\"*&,&F$!\"
\"*&F$F%%\"yGF%F%F%,&*$)%\"xGF$F%F%F%F(F(F(" }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 0 "" }}}}}{SECT 1 {PARA 0 "" 0 "" {TEXT 260 2 "4." }
{TEXT -1 25 " Consider the polynomial " }{XPPEDIT 18 0 "(2*x^2-x)*(2*x
^2+x)" "6#*&,&*&\"\"#\"\"\"*$%\"xGF&F'F'F)!\"\"F',&*&F&F'*$F)F&F'F'F)F
'F'" }{TEXT -1 21 ".\nTransform it into:\n" }{TEXT 273 3 "(a)" }{TEXT 
-1 3 "   " }{XPPEDIT 18 0 "(-1+4*x^2)*x^2" "6#*&,&\"\"\"!\"\"*&\"\"%F%
*$%\"xG\"\"#F%F%F%*$F*F+F%" }{TEXT -1 2 "\n\n" }{TEXT 274 3 "(b)" }
{TEXT -1 3 "   " }{XPPEDIT 18 0 "x^2*(2*x-1)*(2*x+1)" "6#*(%\"xG\"\"#,
&*&F%\"\"\"F$F(F(F(!\"\"F(,&*&F%F(F$F(F(F(F(F(" }{TEXT -1 2 "\n\n" }
{TEXT 275 3 "(c)" }{TEXT -1 3 "   " }{XPPEDIT 18 0 "(2*x^3+x^2)*(2*x-1
)" "6#*&,&*&\"\"#\"\"\"*$%\"xG\"\"$F'F'*$F)F&F'F',&*&F&F'F)F'F'F'!\"\"
F'" }{TEXT -1 1 "\n" }}{SECT 1 {PARA 5 "" 0 "" {TEXT 276 3 "(a)" }}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 28 "expr := (2*x^2-x)*(2*x^2+x);" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#>%%exprG*&,&*&\"\"#\"\"\")%\"xGF(F)F)F+!\"\"F),&*&
F(F)F*F)F)F+F)F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "expand(
expr);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*&\"\"%\"\"\")%\"xGF%F&F&*
$)F(\"\"#F&!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "algsubs
(x^2=y, %);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*&\"\"%\"\"\")%\"yG\"
\"#F&F&F(!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "factor(%)
;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&%\"yG\"\"\",&*&\"\"%F%F$F%F%F%!
\"\"F%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "subs(y=x^2, %);" 
}}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&)%\"xG\"\"#\"\"\",&*&\"\"%F'F$F'F'
F'!\"\"F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 
{PARA 5 "" 0 "" {TEXT 277 3 "(b)" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 8 "restart;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "expr := \+
(2*x^2-x)*(2*x^2+x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%exprG*&,&*&
\"\"#\"\"\")%\"xGF(F)F)F+!\"\"F),&*&F(F)F*F)F)F+F)F)" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 13 "factor(expr);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#*()%\"xG\"\"#\"\"\",&*&F&F'F%F'F'F'!\"\"F',&*&F&F'F%F'F
'F'F'F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 
{PARA 5 "" 0 "" {TEXT 278 3 "(c)" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 8 "restart;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "expr := \+
(2*x^2-x)*(2*x^2+x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%exprG*&,&*&
\"\"#\"\"\")%\"xGF(F)F)F+!\"\"F),&*&F(F)F*F)F)F+F)F)" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 13 "factor(expr);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#*()%\"xG\"\"#\"\"\",&*&F&F'F%F'F'F'!\"\"F',&*&F&F'F%F'F
'F'F'F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "subs(2*x-1=y, %)
;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*()%\"xG\"\"#\"\"\"%\"yGF',&*&F&F
'F%F'F'F'F'F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "collect(%,
 y, expand);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&,&*&\"\"#\"\"\")%\"x
G\"\"$F'F'*$)F)F&F'F'F'%\"yGF'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 17 "subs(y=2*x-1, %);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&,&*&\"
\"#\"\"\")%\"xG\"\"$F'F'*$)F)F&F'F'F',&*&F&F'F)F'F'F'!\"\"F'" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}}{SECT 1 {PARA 0 "" 0 "
" {TEXT 279 2 "5." }{TEXT -1 25 " Consider the polynomial " }{XPPEDIT 
18 0 "(x^2 + x * y + x + y) * (x + y)" "6#*&,**$%\"xG\"\"#\"\"\"*&F&F(
%\"yGF(F(F&F(F*F(F(,&F&F(F*F(F(" }{TEXT -1 22 ". \nTransform it into:
\n" }{TEXT 280 3 "(a)" }{TEXT -1 3 "   " }{XPPEDIT 18 0 "x^3+2*x^2*y+x
*y^2+x^2+2*x*y+y^2" "6#,.*$%\"xG\"\"$\"\"\"*(\"\"#F'*$F%F)F'%\"yGF'F'*
&F%F'*$F+F)F'F'*$F%F)F'*(F)F'F%F'F+F'F'*$F+F)F'" }{TEXT -1 2 "\n\n" }
{TEXT 281 3 "(b)" }{TEXT -1 3 "   " }{XPPEDIT 18 0 "(x+1)*(x+y)^2" "6#
*&,&%\"xG\"\"\"F&F&F&*$,&F%F&%\"yGF&\"\"#F&" }{TEXT -1 2 "\n\n" }
{TEXT 282 3 "(c)" }{TEXT -1 3 "   " }{XPPEDIT 18 0 "y^2+(2*y+y^2)*x+(1
+2*y)*x^2+x^3" "6#,**$%\"yG\"\"#\"\"\"*&,&*&F&F'F%F'F'*$F%F&F'F'%\"xGF
'F'*&,&F'F'*&F&F'F%F'F'F'*$F,F&F'F'*$F,\"\"$F'" }{TEXT -1 2 "\n\n" }
{TEXT 283 3 "(d)" }{TEXT -1 3 "   " }{XPPEDIT 18 0 "x^3+x^2+(2*x^2+2*x
)*y+(x+1)*y" "6#,**$%\"xG\"\"$\"\"\"*$F%\"\"#F'*&,&*&F)F'*$F%F)F'F'*&F
)F'F%F'F'F'%\"yGF'F'*&,&F%F'F'F'F'F/F'F'" }{TEXT -1 1 "\n" }}{SECT 1 
{PARA 5 "" 0 "" {TEXT 284 3 "(a)" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 8 "restart;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "poly := \+
(x^2+x*y+x+y)*(x+y);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%polyG*&,**$
)%\"xG\"\"#\"\"\"F+*&F)F+%\"yGF+F+F)F+F-F+F+,&F)F+F-F+F+" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "expand(poly);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#,.*$)%\"xG\"\"$\"\"\"F(*(\"\"#F()F&F*F(%\"yGF(F(*&F&F()
F,F*F(F(*$F+F(F(*(F*F(F&F(F,F(F(*$F.F(F(" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 5 "" 0 "" {TEXT 285 3 "(b)" }}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 28 "poly := (x^2+x*y+x+y)*(x+y);" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#>%%polyG*&,**$)%\"xG\"\"#\"\"\"F+*&F)F+%\"yGF+F+F)
F+F-F+F+,&F)F+F-F+F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "fac
tor(poly);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&,&%\"xG\"\"\"F&F&F&),&
F%F&%\"yGF&\"\"#F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}
{SECT 1 {PARA 5 "" 0 "" {TEXT 286 3 "(c)" }}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 8 "restart;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 
"poly := (x^2+x*y+x+y)*(x+y);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%po
lyG*&,**$)%\"xG\"\"#\"\"\"F+*&F)F+%\"yGF+F+F)F+F-F+F+,&F)F+F-F+F+" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "collect(poly, x, expand);" }
}{PARA 11 "" 1 "" {XPPMATH 20 "6#,**$)%\"xG\"\"$\"\"\"F(*&,&*&\"\"#F(%
\"yGF(F(F(F(F()F&F,F(F(*&,&*&F,F(F-F(F(*$)F-F,F(F(F(F&F(F(F2F(" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "series(%, x); # reordering" 
}}{PARA 11 "" 1 "" {XPPMATH 20 "6#++%\"xG*$)%\"yG\"\"#\"\"\"\"\"!,&*&F
(F)F'F)F)F%F)F),&*&F(F)F'F)F)F)F)F(F)\"\"$" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 5 "" 0 "" {TEXT 287 3 "(d)" }}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 28 "poly := (x^2+x*y+x+y)*(x+y);" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#>%%polyG*&,**$)%\"xG\"\"#\"\"\"F+*&F)F+%\"yGF+F+F)
F+F-F+F+,&F)F+F-F+F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "col
lect(poly, y, expand);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,**&,&%\"xG
\"\"\"F'F'F')%\"yG\"\"#F'F'*&,&*&F*F')F&F*F'F'*&F*F'F&F'F'F'F)F'F'*$)F
&\"\"$F'F'*$F.F'F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "serie
s(%, y); # reordering" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#+)%\"yG,&*$)%
\"xG\"\"$\"\"\"F**$)F(\"\"#F*F*\"\"!,&*&F-F*F,F*F**&F-F*F(F*F*F*,&F(F*
F*F*F-" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}}}{MARK "0" 
0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }