{VERSION 3 0 "IBM INTEL NT" "3.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 }{CSTYLE "2D Comment" 2 18 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 } {CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 }{CSTYLE " " 18 256 "" 0 1 255 0 0 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 257 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 258 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 259 "" 0 1 255 0 0 1 0 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 260 "" 0 1 255 0 0 1 0 0 0 0 0 0 0 0 0 }{PSTYLE "Normal " -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Heading 1" 0 3 1 {CSTYLE "" -1 -1 "" 1 18 0 0 0 0 0 1 0 0 0 0 0 0 0 }1 0 0 0 8 4 0 0 0 0 0 0 -1 0 }{PSTYLE "Heading 2" 3 4 1 {CSTYLE "" -1 -1 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 } 0 0 0 -1 8 2 0 0 0 0 0 0 -1 0 }{PSTYLE "Heading 3" 4 5 1 {CSTYLE "" -1 -1 "" 1 12 0 0 0 0 1 0 0 0 0 0 0 0 0 }0 0 0 -1 0 0 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple Output" 0 11 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 3 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 11 12 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }1 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Title" 0 18 1 {CSTYLE "" -1 -1 "" 1 18 0 0 0 0 0 1 1 0 0 0 0 0 0 }3 0 0 -1 12 12 0 0 0 0 0 0 19 0 }{PSTYLE "Author" 0 19 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 0 0 -1 8 8 0 0 0 0 0 0 -1 0 }} {SECT 0 {EXCHG {PARA 18 "" 0 "" {TEXT -1 17 "Termumformungen 1" }} {PARA 19 "" 0 "" {TEXT -1 46 "HGB 27.8.99 Datei: ML-04 Termumformungen 1.mws" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 58 "Wir kennen alle die Bin omische Formel (aus der Klasse 8): " }{XPPEDIT 256 0 "(a+b)^2 = a^2+2* ab+b^2;" "6#/*$,&%\"aG\"\"\"%\"bGF'\"\"#,(*$F&\"\"#F'*&\"\"#F'%#abGF'F '*$F(\"\"#F'" }{TEXT -1 2 " ." }}{PARA 0 "" 0 "" {TEXT -1 11 "Man muss te " }{TEXT 257 17 "ausmultiplizieren" }{TEXT -1 43 " (aus einem Produ kt eine Summe machen) und " }{TEXT 258 13 "faktorisieren" }{TEXT -1 38 " (aus einer Summe ein Produkt machen)." }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 8 "restart;" }{TEXT -1 135 "Jedes Worksheet beginnen wi r ab jetzt damit, damit uns nicht eine Variable aus einem anderen ge \366ffneten Worksheet einen Streich spielt." }}}{SECT 0 {PARA 3 "" 0 " " {TEXT -1 29 "Ausmultiplizieren mit Maple: " }{TEXT 259 6 "expand" }} {SECT 1 {PARA 4 "" 0 "" {TEXT -1 37 "Kann Maple die Binomischen Formel n ??" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "expand ((a+b)^2);" } }{PARA 11 "" 1 "" {XPPMATH 20 "6#,(*$)%\"aG\"\"#\"\"\"\"\"\"*&F&F)%\"b GF)F'*$)F+F'F(F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "expand \+ ((a-b)^2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,(*$)%\"aG\"\"#\"\"\"\" \"\"*&F&F)%\"bGF)!\"#*$)F+F'F(F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "expand((a+b)*(a-b));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*$)%\"aG\"\"#\"\"\"\"\"\"*$)%\"bGF'F(!\"\"" }}}}{SECT 0 {PARA 4 " " 0 "" {TEXT -1 17 "Weitere Beispiele" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "expand ((x+y)^4);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6# ,,*$)%\"xG\"\"%\"\"\"\"\"\"*&)F&\"\"$F(%\"yGF)F'*&)F&\"\"#F()F-F0F(\" \"'*&F&F))F-F,F(F'*$)F-F'F(F)" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 20 " Andere Schreibweise:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "t1:= x*(x-a )^2*(x-b)^3;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#t1G*(%\"xG\"\"\"),& F&F'%\"aG!\"\"\"\"#\"\"\"),&F&F'%\"bGF+\"\"$F-" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 11 "expand(t1);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6 #,:*$)%\"xG\"\"'\"\"\"\"\"\"*&)F&\"\"&F(%\"bGF)!\"$*&)F&\"\"%F()F-\"\" #F(\"\"$*&)F&F4F()F-F4F(!\"\"*&F+F(%\"aGF)!\"#*(F0F(F:F(F-F(F'*(F6F(F: F(F2F(!\"'*()F&F3F(F:F(F7F(F3*&)F:F3F(F0F(F)*(FBF(F6F(F-F(F.*(FBF(F@F( F2F(F4*(F&F)FBF(F7F(F8" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "t 1=expand(t1);" }{TEXT -1 146 "beachte die Schreibweise: Wir haben eine Gleichung geschaffen (keine Zuordnung zu einer Variablen; dort m\374 \337te ja vor dem = ein Doppelpunkt stehen." }}{PARA 12 "" 1 "" {XPPMATH 20 "6#/*(%\"xG\"\"\"),&F%F&%\"aG!\"\"\"\"#\"\"\"),&F%F&%\"bGF *\"\"$F,,:*$)F%\"\"'F,F&*&)F%\"\"&F,F/F&!\"$*&)F%\"\"%F,)F/F+F,F0*&)F% F0F,)F/F0F,F**&F6F,F)F&!\"#*(F:F,F)F,F/F,F4*(F>F,F)F,FF,F/F,F8*(FHF,FFF,F " 0 "" {MPLTEXT 1 0 13 "expand(5*t1);" }} {PARA 12 "" 1 "" {XPPMATH 20 "6#,:*$)%\"xG\"\"'\"\"\"\"\"&*&)F&F)F(%\" bG\"\"\"!#:*&)F&\"\"%F()F,\"\"#F(\"#:*&)F&\"\"$F()F,F7F(!\"&*&F+F(%\"a GF-!#5*(F0F(F;F(F,F(\"#I*(F6F(F;F(F2F(!#I*()F&F3F(F;F(F8F(\"#5*&)F;F3F (F0F(F)*(FEF(F6F(F,F(F.*(FEF(FBF(F2F(F4*(F&F-FEF(F8F(F9" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "5*t1;" }{TEXT -1 41 "Warum steht nun ein anderes Ergebnis da ?" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*(%\"x G\"\"\"),&F%F&%\"aG!\"\"\"\"#\"\"\"),&F%F&%\"bGF*\"\"$F,\"\"&" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "t3:=(x-1)^2+(x+4)^2;t3=expan d(%);" }{TEXT -1 31 "auch Summen werden verarbeitet." }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#t3G,&*$),&%\"xG\"\"\"!\"\"F*\"\"#\"\"\"F**$),&F)F *\"\"%F*F,F-F*" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/,&*$),&%\"xG\"\"\"! \"\"F)\"\"#\"\"\"F)*$),&F(F)\"\"%F)F+F,F),(*$)F(F+F,F+F(\"\"'\"# \+ " 0 "" {MPLTEXT 1 0 22 "factor(a^2+2*a*b+b^2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*$),&%\"aG\"\"\"%\"bGF'\"\"#\"\"\"" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 22 "factor(a^2-2*a*b+b^2);" }{TEXT -1 56 "Hier i st kopieren geschickt; dann das + durch - ersetzen" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#*$),&%\"bG\"\"\"%\"aG!\"\"\"\"#\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "factor(a^2-b^2);" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#,$*&,&%\"bG\"\"\"%\"aG!\"\"F',&F(F'F&F'F'F)" }}}} {SECT 1 {PARA 5 "" 0 "" {TEXT -1 17 "Weitere Beispiele" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "T1:=expand(t1);" }}{PARA 12 "" 1 " " {XPPMATH 20 "6#>%#T1G,:*$)%\"xG\"\"'\"\"\"\"\"\"*&)F(\"\"&F*%\"bGF+! \"$*&)F(\"\"%F*)F/\"\"#F*\"\"$*&)F(F6F*)F/F6F*!\"\"*&F-F*%\"aGF+!\"#*( F2F*F " 0 "" {MPLTEXT 1 0 12 "factor (T1);" }{TEXT -1 49 "Das h\344tten wir lo cker mit der Hand gemacht oder ?" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*( %\"xG\"\"\"),&F$F%%\"aG!\"\"\"\"#\"\"\"),&F$F%%\"bGF)\"\"$F+" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "t2:=16*s^4-64*r^4;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#t2G,&*$)%\"sG\"\"%\"\"\"\"#;*$)%\"rGF)F*! #k" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "factor(t2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*&,&*$)%\"sG\"\"#\"\"\"\"\"\"*$)%\"rGF)F*! \"#F+,&F&F+F,F)F+\"#;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "ex pand(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*$)%\"sG\"\"%\"\"\"\"#;* $)%\"rGF'F(!#k" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "factor(x^ 2-2*x+1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*$),&%\"xG\"\"\"!\"\"F'\" \"#\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "factor(x^3-6*x ^2+3*x+10);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*(,&%\"xG\"\"\"!\"&F&F& ,&F%F&!\"#F&F&,&F%F&F&F&F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "factor(x^3-2*x^2-x);" }{TEXT -1 40 " Warum erfolgt keine weitere Z erlegung ?" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&%\"xG\"\"\",(*$)F$\"\" #\"\"\"F%F$!\"#!\"\"F%F%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "factor(x^4-7*x^2+12);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*(,&%\"xG\" \"\"!\"#F&F&,&F%F&\"\"#F&F&,&*$)F%F)\"\"\"F&!\"$F&F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "factor(x^3-6*x^2+11*x-6);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*(,&%\"xG\"\"\"!\"\"F&F&,&F%F&!\"#F&F&,&F%F&!\"$F& F&" }}}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 7 "Grenzen" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "t3:=(x-2)^3/(x+4)^2;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#t3G*&*$),&%\"xG\"\"\"!\"#F*\"\"$\"\"\"F-*$),&F)F*\" \"%F*\"\"#F-!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "t4:=ex pand(t3);" }{TEXT -1 75 "Wo ist die Grenze ? Wie unterscheidet sich di eser Term von den bisherigen ?" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#t 4G,**&*$)%\"xG\"\"$\"\"\"F+*$),&F)\"\"\"\"\"%F/\"\"#F+!\"\"F/*&*$)F)\" \"#F+F+*$)F.\"\"#F+F2!\"'*&F)F+*$)F.\"\"#F+F2\"#7*&F+F+*$)F.\"\"#F+F2! \")" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "factor(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&*$),&%\"xG\"\"\"!\"#F(\"\"$\"\"\"F+*$),&F' F(\"\"%F(\"\"#F+!\"\"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 71 "Wir h \344tten t4 gerne einfacher, eben simpel. Der Befehl liegt also nahe. " }{TEXT -1 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "simplify(t4);" } }{PARA 11 "" 1 "" {XPPMATH 20 "6#*&,**$)%\"xG\"\"$\"\"\"\"\"\"*$)F'\" \"#F)!\"'F'\"#7!\")F*F)*$),&F'F*\"\"%F*\"\"#F)!\"\"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 46 "An den Nenner sind wir aber nicht rangekommen. " }}}}}{MARK "3 2 4 0 1" 138 }{VIEWOPTS 1 1 0 1 1 1803 }