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-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 O utput" 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 "Heading 4" 5 20 1 {CSTYLE "" -1 -1 "" 1 10 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 "" 11 256 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 "" 0 257 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 } {PSTYLE "" 4 258 1 {CSTYLE "" -1 -1 "" 0 12 0 0 0 0 0 2 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 259 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 } {PSTYLE "" 3 260 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 1 0 -1 0 }} {SECT 0 {SECT 0 {PARA 260 "" 0 "" {TEXT 257 33 "Section 2: Algebraic C alculations" }{TEXT -1 1 " " }}{PARA 0 "" 0 "" {TEXT 256 30 "Maple is \+ a \"C.A.S\" , i.e. a " }{TEXT 333 1 "C" }{TEXT 334 8 "omputer " } {TEXT 335 1 "A" }{TEXT 336 7 "lgebra " }{TEXT 337 1 "S" }{TEXT 338 261 "ystem. This means that Maple knows every rule of algebra that you know. As you progress through Calculus, Differential Equations and Li near Algebra you will find that Maple also has the essential operation s from those subjects built into its large command set. " }}{PARA 0 " " 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 332 204 "In this section \+ you will learn how to enter an algebraic expression and substitute val ues in for the variables. Then you will learn the commands that allow \+ you to expand, factor and simplify expressions. " }}{PARA 0 "" 0 "" {TEXT -1 33 "Place the cursor anywhere on the " }{TEXT 353 7 "restart " }{TEXT -1 41 " command and hit enter before continuing." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 0 "" }}}{SECT 1 {PARA 4 "" 0 "subs( )" {TEXT -1 4 "The " }{TEXT 339 7 "subs( )" }{TEXT -1 8 " command" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 322 10 "Example 1:" }}{PARA 0 " " 0 "" {TEXT -1 55 "For our first example let's start with the express ion " }{XPPEDIT 18 0 "3*x^2+8" "6#,&*&\"\"$\"\"\"*$%\"xG\"\"#F&F&\"\" )F&" }{TEXT -1 28 " and assign it the name W. " }}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 11 "W:=3*x^2+8;" }}}{PARA 0 "" 0 "" {TEXT -1 77 "S uppose now that you want to substitute the value 4 for x in the expres sion " }{XPPEDIT 18 0 "3x^2+8" "6#,&*&\"\"$\"\"\"*$%\"xG\"\"#F&F&\"\" )F&" }{TEXT -1 48 ". The quickest way to do this is to use Maple's " } {TEXT 298 7 "subs( )" }{TEXT -1 36 " command. Here's what it looks lik e:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "subs(x=4,3*x^2+8);" }} }{PARA 0 "" 0 "" {TEXT -1 32 "Alternatively you can apply the " } {TEXT 299 7 "subs( )" }{TEXT -1 14 " command to W." }}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 12 "subs(x=4,W);" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 323 10 "Example 2:" }}{PARA 0 "" 0 "" {TEXT -1 4 "The " }{TEXT 324 7 "subs( )" }{TEXT -1 49 " command works \+ equally well with symbolic values:" }}{PARA 0 "" 0 "" {TEXT -1 17 "To \+ replace x by " }{XPPEDIT 18 0 "5+2*u" "6#,&\"\"&\"\"\"*&\"\"#F%%\"uGF %F%" }{TEXT -1 19 " in the expression " }{XPPEDIT 18 0 "3*x^2+8" "6#,& *&\"\"$\"\"\"*$%\"xG\"\"#F&F&\"\")F&" }{TEXT -1 64 " execute the follo wing line. In this case we label the result M." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "W:=3*x^2+8;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "M:=subs(x=5+2*u,W);" }}}{PARA 0 "" 0 "" {TEXT -1 67 " And now to get Maple to \"multiply out\" this expression we use the \+ " }{TEXT 297 9 "expand( )" }{TEXT -1 11 " command. " }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "expand(M);" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 325 10 "Example 3:" }}{PARA 0 "" 0 "" {TEXT -1 4 "The " }{TEXT 300 7 "subs( )" }{TEXT -1 101 " command is ve ry versatile. You can use it to evaluate expressions involving more t han one variable." }{MPLTEXT 1 0 1 " " }{TEXT -1 17 "Here we replace \+ " }{XPPEDIT 18 0 "x" "6#%\"xG" }{TEXT -1 39 " by 7 and y by 12 in the expression " }{XPPEDIT 18 0 " U=2/5*x^2+3*y" "6#/%\"UG,&*(\"\"#\"\" \"\"\"&!\"\"%\"xG\"\"#F(*&\"\"$F(%\"yGF(F(" }{TEXT -1 4 " . " }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "U:=(2/5)*x^2+3*y;" }}{PARA 0 "" 0 "" {TEXT -1 8 " " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "subs(x=7,y=12,U);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "evalf(%);" }}}{PARA 0 "" 0 "" {TEXT 326 10 "Example 4:" }}{PARA 0 "" 0 "" {TEXT -1 21 "You can also use the " }{TEXT 327 7 "subs( )" } {TEXT -1 229 " command to substitute a value into an equation. This is the sort of thing you might want to do to test whether a particular v alue \"satisfies\" the equation. In the next few lines we substitute d ifferent values into the equation " }{XPPEDIT 18 0 "x^3-5*x^2+7*x-12= 0" "6#/,**$%\"xG\"\"$\"\"\"*&\"\"&F(*$F&\"\"#F(!\"\"*&\"\"(F(F&F(F(\"# 7F-\"\"!" }{TEXT -1 55 " . Are any of these values a solution to the \+ equation?" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 77 "Note we use \" := \" to assign the name and just \"=\" for the e quation itself." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "eqn:=x^3- 5*x^2+7*x-12=0;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "subs(x=3 ,eqn);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "subs(x=4,eqn);" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "subs(x=5,eqn);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{SECT 1 {PARA 4 "" 0 "" {TEXT 288 12 "Exercise 2.1" }}{PARA 0 "" 0 "" {TEXT -1 38 "Assign the name k to the expression " }{XPPEDIT 18 0 "x^2+4*x-3" "6#,(*$%\"xG\"\"#\" \"\"*&\"\"%F'F%F'F'\"\"$!\"\"" }{TEXT -1 45 " . Then assign the name M to the expression " }{XPPEDIT 18 0 "k^2-9" "6#,&*$%\"kG\"\"#\"\"\"\" \"*!\"\"" }{TEXT -1 1 "." }}{PARA 0 "" 0 "" {TEXT -1 31 "Finally have \+ Maple calculate " }{XPPEDIT 18 0 "3*M+6" "6#,&*&\"\"$\"\"\"%\"MGF&F& \"\"'F&" }{TEXT -1 61 " . Note: to get Maple to multiply the expressio n out use the " }{TEXT 296 10 "expand( ) " }{TEXT -1 110 "command. Tha t is enter: expand(3*M+6); You will learn more about the expand com mand in the next subsection." }}{PARA 0 "" 0 "" {TEXT 289 2 " " }} {SECT 1 {PARA 20 "" 0 "" {TEXT 290 21 "Student Workspace 2.1" }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}} }{SECT 1 {PARA 4 "" 0 "" {TEXT 293 12 "Exercise 2.2" }}{PARA 0 "" 0 " " {TEXT -1 8 "Expand " }{XPPEDIT 18 0 "( 1+x)^4" "6#*$,&\"\"\"\"\"\"% \"xGF&\"\"%" }{TEXT -1 11 " using the " }{TEXT 352 9 "expand( )" } {TEXT -1 11 " command. " }}{SECT 1 {PARA 20 "" 0 "" {TEXT 294 21 "Stu dent Workspace 2.2" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}} }{SECT 1 {PARA 258 "" 0 "" {TEXT 301 12 "Exercise 2.3" }}{PARA 4 "" 0 "" {TEXT 302 4 "Let " }{XPPEDIT 321 0 "P=ax^3+bx^2+c*x+d" "6#/%\"PG,** $%#axG\"\"$\"\"\"*$%#bxG\"\"#F)*&%\"cGF)%\"xGF)F)%\"dGF)" }{TEXT 320 7 " . Find" }{TEXT 318 1 " " }{TEXT 319 5 "P if" }{TEXT 304 1 " " } {TEXT 303 16 " x = 0.01 , a =" }{TEXT 314 1 " " }{XPPEDIT 309 0 "(-1/ 5)" "6#,$*&\"\"\"\"\"\"\"\"&!\"\"F(" }{TEXT 308 1 " " }{TEXT 315 2 ", \+ " }{XPPEDIT 311 0 "b=2/5" "6#/%\"bG*&\"\"#\"\"\"\"\"&!\"\"" }{TEXT 310 2 ", " }{XPPEDIT 313 0 "c=0" "6#/%\"cG\"\"!" }{TEXT 312 6 ", and \+ " }}{PARA 4 "" 0 "" {TEXT 307 1 " " }{XPPEDIT 316 0 "d=13/15" "6#/%\"d G*&\"#8\"\"\"\"#:!\"\"" }{TEXT 317 3 " ." }}{SECT 1 {PARA 20 "" 0 "" {TEXT 305 21 "Student Workspace 2.3" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 0 "" }}}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{SECT 1 {PARA 4 "" 0 "" {TEXT 330 12 "Exercise 2.4" }}{PARA 0 "" 0 "" {TEXT -1 8 "Use the " }{TEXT 331 7 "subs( )" }{TEXT -1 80 " command to check if any of the numbers: 1,2 or 3 is a solution to the equation:" }} {PARA 259 "" 0 "" {TEXT -1 1 " " }{XPPEDIT 18 0 "x^3-16*x^2+51*x-36=0 " "6#/,**$%\"xG\"\"$\"\"\"*&\"#;F(*$F&\"\"#F(!\"\"*&\"#^F(F&F(F(\"#OF- \"\"!" }{TEXT -1 2 " " }}{SECT 1 {PARA 20 "" 0 "" {TEXT 328 21 "Stude nt Workspace 2.4" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}} }}{SECT 1 {PARA 4 "" 0 "expand( )" {TEXT -1 4 "The " }{TEXT 340 9 "ex pand( )" }{TEXT -1 8 " command" }}{PARA 0 "" 0 "" {TEXT -1 25 "The pri ncipal use of the " }{TEXT 278 10 "expand( ) " }{TEXT -1 144 "command \+ is to \"multiply out\" products of polynomial expressions. It can also be used to expand trigonometric and other more general functions. " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 279 10 "Exampl e 1:" }}{PARA 0 "" 0 "" {TEXT -1 8 "Use the " }{TEXT 281 9 "expand( ) " }{TEXT -1 27 " command to multiply out " }{XPPEDIT 18 0 "(x+2)^2*( 3x-3)*(x+5)" "6#*(,&%\"xG\"\"\"\"\"#F&\"\"#,&*&\"\"$F&F%F&F&\"\"$!\"\" F&,&F%F&\"\"&F&F&" }{TEXT -1 2 " ." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "k:=(x+2)^2*(3*x-3)*(x+5);" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "expand(k);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT 280 10 "E xample 2:" }}{PARA 0 "" 0 "" {TEXT -1 63 "Maple applies some familiar \+ trigonometric identities to expand " }{XPPEDIT 18 0 "sin(2*x)" "6#-%$s inG6#*&\"\"#\"\"\"%\"xGF(" }{TEXT -1 5 " and " }{XPPEDIT 18 0 "cos(2*x )" "6#-%$cosG6#*&\"\"#\"\"\"%\"xGF(" }{TEXT -1 2 " ." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "expand(sin(2*x));" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 17 "expand(cos(2*x));" }}}{PARA 0 "" 0 "" {TEXT -1 85 "Try expanding the sine and cosine of some other integer multipl es of x. For example: " }{XPPEDIT 18 0 "sin(3*x)" "6#-%$sinG6#*&\"\"$ \"\"\"%\"xGF(" }{TEXT -1 3 " , " }{XPPEDIT 18 0 "cos(6*x)" "6#-%$cosG6 #*&\"\"'\"\"\"%\"xGF(" }{TEXT -1 7 " , etc." }}{PARA 0 "" 0 "" {TEXT 286 10 "Example 3:" }}{PARA 0 "" 0 "" {TEXT -1 67 "Here is a final exa mple. Have Maple multiply out the expression: " }{XPPEDIT 18 0 "x^(1 /2)*(x^(3/2)+x^(-1/2))" "6#*&)%\"xG*&\"\"\"\"\"\"\"\"#!\"\"F(,&)F%*&\" \"$F(\"\"#F*F()F%,$*&\"\"\"F(\"\"#F*F*F(F(" }}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 30 "h:=x^(1/2)*(x^(3/2)+x^(-1/2));" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 10 "expand(h);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{SECT 1 {PARA 4 " " 0 "" {TEXT 283 12 "Exercise 2.6" }}{PARA 0 "" 0 "" {TEXT 282 8 "Expa nd " }{XPPEDIT 18 0 "( x +1 )^n" "6#),&%\"xG\"\"\"\"\"\"F&%\"nG" } {TEXT 285 20 " for n =2,3 and 4. " }}{SECT 1 {PARA 20 "" 0 "" {TEXT 284 21 "Student Workspace 2.6" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}} {SECT 1 {PARA 4 "" 0 "factor( )" {TEXT -1 4 "The " }{TEXT 341 9 "fact or( )" }{TEXT -1 8 " command" }}{PARA 0 "" 0 "" {TEXT 263 10 "Example \+ 1:" }}{PARA 0 "" 0 "" {TEXT -1 23 "Factor the expression: " }{XPPEDIT 18 0 "3*x^2-10*x-8" "6#,(*&\"\"$\"\"\"*$%\"xG\"\"#F&F&*&\"#5F&F(F&!\" \"\"\")F," }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "w:=3*x^2-10*x-8 ;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "factor(w);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 33 "Or you can do it all on one line:" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "factor(3*x^2-10*x-8);" }}} {PARA 0 "" 0 "" {TEXT 266 10 "Example 2:" }}{PARA 0 "" 0 "" {TEXT -1 29 "First expand the expression " }{XPPEDIT 18 0 "2*(x-2)*(2*x^2+5*x+ 2)*(x+4)" "6#**\"\"#\"\"\",&%\"xGF%\"\"#!\"\"F%,(*&\"\"#F%*$F'\"\"#F%F %*&\"\"&F%F'F%F%\"\"#F%F%,&F'F%\"\"%F%F%" }{TEXT -1 19 " . Then apply the " }{TEXT 287 9 "factor( )" }{TEXT -1 107 " command to the result. Can you explain why the final result looks different than the origina l expression ?" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "H:=2*(x-2) *(2*x^2+5*x+2)*(x+4);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "an s:=expand(H);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "factor(ans );" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 264 10 "E xample 3:" }}{PARA 0 "" 0 "" {TEXT -1 57 "Maple can factor expressions with more than one variable." }}{PARA 0 "" 0 "" {TEXT -1 25 "Factor t he expression: " }{XPPEDIT 18 0 "x^2y+2xy+y" "6#,(*&%\"xG\"\"#%\"yG \"\"\"F(*&\"\"#F(%#xyGF(F(F'F(" }}{PARA 11 "" 1 "" {TEXT -1 0 "" }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "h:=x^2*y+2*x*y+y;" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "factor(h);" }}}{PARA 0 "" 0 "" {TEXT 265 10 "Example 4:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 125 "If Maple can't factor an expression using rati onal numbers (i.e. integers and fractions) then it returns the input u nchanged." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "factor(3*x^2-10 *x-9);" }}}{PARA 0 "" 0 "" {TEXT 267 10 "Example 5:" }}{PARA 0 "" 0 " " {TEXT -1 87 "The factor command is not limited to polynomials. It ca n be used to factor other forms." }}{PARA 0 "" 0 "" {TEXT -1 7 "Factor " }{XPPEDIT 18 0 "sin^2x -cos^2x:" "6#,&*&%$sinG\"\"#%\"xG\"\"\"F(* &%$cosG\"\"#F'F(!\"\"" }{TEXT -1 2 " ." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "factor((sin(x))^2-(cos(x)^2));" }}}{PARA 0 "" 0 "" {TEXT 268 10 "Example 6:" }}{PARA 0 "" 0 "" {TEXT -1 166 "If the facto r command is used with a rational expression, the numerator and denomi nator are each factored and common factors are cancelled to simplify t he expression:" }{MPLTEXT 1 0 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "A:=(x^3-7*x^2+15*x-9)/(x^2+4*x+4);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "factor(A);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "B:=(x^3-7*x^2+15*x-9)/(x^2-4*x+3);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "factor(B);" }}}{PARA 0 "" 0 "" {TEXT -1 74 "The next example allows you to see the factored form without cance llation." }}{PARA 0 "" 0 "" {TEXT 349 10 "Example 7:" }}{PARA 0 "" 0 " " {TEXT -1 8 "Maple's " }{TEXT 350 8 "numer( )" }{TEXT -1 5 " and " } {TEXT 351 9 "denom( ) " }{TEXT -1 220 "commands allow you to isolate e ither the numerator or denominator of a fraction. Here we use these co mmands to examine the factors of the numerator and denominator separat ely (i.e. before cancellation of common factors)." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "B:=(x^3-7*x^2+15*x-9)/(x^2-4*x+3);" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "factor(numer(B)); factor(de nom(B));" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{SECT 1 {PARA 4 "" 0 "" {TEXT 259 12 "Exercise 2.8" }}{PARA 0 "" 0 "" {TEXT -1 22 "Factor the \+ expression " }{XPPEDIT 18 0 "3x^4-2x^3+22x^2-18x-45 " "6#,,*&\"\"$\"\" \"*$%\"xG\"\"%F&F&*&\"\"#F&*$F(\"\"$F&!\"\"*&\"#AF&*$F(\"\"#F&F&*&\"#= F&F(F&F.\"#XF." }{TEXT -1 2 " ." }}{SECT 1 {PARA 20 "" 0 "" {TEXT 260 18 "Student Workspace " }{TEXT 343 3 "2.8" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 0 "" }}}}}{SECT 1 {PARA 4 "" 0 "" {TEXT 261 12 "Exercis e 2.9" }}{PARA 0 "" 0 "" {TEXT -1 25 "Factor the expression " } {XPPEDIT 18 0 "x^(1/2)-x^(3/2" "6#,&)%\"xG*&\"\"\"\"\"\"\"\"#!\"\"F()F %*&\"\"$F(\"\"#F*F*" }{TEXT -1 59 " and then use the expand comma nd to check the result. " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{SECT 1 {PARA 20 "" 0 "" {TEXT 262 18 "Student Workspace " }{TEXT 345 3 "2.9" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 0 "" }}}}}}{SECT 1 {PARA 4 "" 0 "simplify( )" {TEXT -1 4 "The " }{TEXT 342 11 "simplify( )" }{TEXT -1 8 " command" }} {PARA 0 "" 0 "" {TEXT 269 10 "Example 1:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 258 24 "Consider the expression " } {XPPEDIT 18 0 "cos(x)^5 + sin(x)^4 + 2*cos(x)^2 - 2*sin(x)^2 - cos(2*x )" "6#,,*$-%$cosG6#%\"xG\"\"&\"\"\"*$-%$sinG6#F(\"\"%F**&\"\"#F**$-F&6 #F(\"\"#F*F**&\"\"#F**$-F-6#F(\"\"#F*!\"\"-F&6#*&\"\"#F*F(F*F<" } {TEXT -1 116 " . Maple can apply identities to simplify many lengthy m athematical expressions, such as trigonometric expressions. " }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 60 "V:=cos(x)^5 + sin(x)^4 + 2*c os(x)^2 - 2*sin(x)^2 - cos(2*x);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "simplify(V);" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT 270 10 "Example 2:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 137 "Trigonometric expressions with ar guments in multiples of some angle will be simplified to trig function s in the single angle if possible:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "simplify(sin(5*t)+sin(3*t)); " }}}{PARA 256 "" 0 "" {TEXT 271 10 "Example 3:" }}{PARA 0 "" 0 "" {TEXT -1 65 "The simplify( ) command can be used to add rational expre ssions. " }}{PARA 0 "" 0 "" {TEXT -1 17 "Rewrite the sum " }{XPPEDIT 18 0 "1/(x+1)+x/(x-1)" "6#,&*&\"\"\"\"\"\",&%\"xGF&\"\"\"F&!\"\"F&*&F( F&,&F(F&\"\"\"F*F*F&" }{TEXT -1 23 " as a single fraction." }}{PARA 0 "" 0 "" {TEXT -1 1 " " }}{PARA 257 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "M:=(1/(x+1))+(x/(x-1));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "simplify(M);" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 0 "" }}}{SECT 1 {PARA 4 "" 0 "" {TEXT 272 14 "Exer cise 2.11:" }}{PARA 0 "" 0 "" {TEXT -1 24 "Simplify the expression " } {XPPEDIT 18 0 "7/(x+2)+(3*x)/(x+2)^2" "6#,&*&\"\"(\"\"\",&%\"xGF&\"\"# F&!\"\"F&*(\"\"$F&F(F&*$,&F(F&\"\"#F&\"\"#F*F&" }{TEXT -1 1 " " }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{SECT 1 {PARA 20 "" 0 "" {TEXT 277 18 "Student Workspace " }{TEXT 347 4 "2.11" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}}{SECT 1 {PARA 4 "" 0 " " {TEXT 274 13 "Exercise 2.12" }}{PARA 0 "" 0 "" {TEXT -1 24 "How does Maple simplify " }{XPPEDIT 18 0 "sin(3*t)-sin(7*t)" "6#,&-%$sinG6#*& \"\"$\"\"\"%\"tGF)F)-F%6#*&\"\"(F)F*F)!\"\"" }{TEXT -1 102 " ? Whethe r or not this \"simplified\" form is of use to you will depend on what you plan to do with it." }}{PARA 0 "" 0 "" {TEXT 273 1 " " }}{SECT 1 {PARA 20 "" 0 "" {TEXT 275 22 "Student Workspace 2.12" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "0" 0 }{VIEWOPTS 1 1 0 1 1 1803 }