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}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 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 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 }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 1 }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 1 }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 1 }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 1 }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. " }}{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 expression " } {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 "Suppose \+ now that you want to substitute the value 4 for x in the expression \+ " }{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 like:" }} {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 w ell 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 following l ine. 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 very versat ile. You can use it to evaluate expressions involving more than one v ariable." }{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 ex pression " }{XPPEDIT 18 0 " U=2/5*x^2+3*y" "6#/%\"UG,&*(\"\"#\"\"\" \"\"&!\"\"%\"xGF'F(*&\"\"$F(%\"yGF(F(" }{TEXT -1 4 " . " }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "U:=(2/5)*x^2+3*y;" }}{PARA 0 "" 0 " " {TEXT -1 8 " " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "s ubs(x=7,y=12,U);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "evalf(%) ;" }}}{PARA 0 "" 0 "" {TEXT 326 10 "Example 4:" }}{PARA 0 "" 0 "" {TEXT -1 21 "You can also use the " }{TEXT 327 7 "subs( )" }{TEXT -1 229 " command to substitute a value into an equation. This is the sort of thing you might want to do to test whether a particular value \"sa tisfies\" the equation. In the next few lines we substitute different \+ values into the equation " }{XPPEDIT 18 0 "x^3-5*x^2+7*x-12=0" "6#/,* *$%\"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 equation \+ 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 20 "" 0 "" {TEXT 291 10 "Answer 2.1" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "k:=x^2+4*x-3;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "M:=k^2-9;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "3*M+6;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "expand(3*M+6);" }}}{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#*$,&\"\"\"F%%\"xGF%\"\"%" }{TEXT -1 11 " using the " }{TEXT 352 9 "expand( )" }{TEXT -1 11 " command. " } }{SECT 1 {PARA 20 "" 0 "" {TEXT 294 21 "Student Workspace 2.2" }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 20 "" 0 " " {TEXT 295 10 "Answer 2.2" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "w:=(1+x)^4;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "expand(w );" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 40 "or we can do this all in on e step with: " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "expand((1+ x)^4);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}}{SECT 1 {PARA 258 "" 0 "" {TEXT 301 12 "Exercise 2.3" }}{PARA 4 "" 0 "" {TEXT 302 4 "Let " }{XPPEDIT 321 0 "P=ax^3+bx^2+c*x+d" "6#/%\"PG,**$%#axG\" \"$\"\"\"*$%#bxG\"\"#F)*&%\"cGF)%\"xGF)F)%\"dGF)" }{TEXT 320 7 " . Fin d" }{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#,$* &\"\"\"F%\"\"&!\"\"F'" }{TEXT 308 1 " " }{TEXT 315 2 ", " }{XPPEDIT 311 0 "b=2/5" "6#/%\"bG*&\"\"#\"\"\"\"\"&!\"\"" }{TEXT 310 2 ", " } {XPPEDIT 313 0 "c=0" "6#/%\"cG\"\"!" }{TEXT 312 6 ", and " }}{PARA 4 " " 0 "" {TEXT 307 1 " " }{XPPEDIT 316 0 "d=13/15" "6#/%\"dG*&\"#8\"\"\" \"#:!\"\"" }{TEXT 317 3 " ." }}{SECT 1 {PARA 20 "" 0 "" {TEXT 305 21 "Student Workspace 2.3" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} }{SECT 1 {PARA 20 "" 0 "" {TEXT 306 10 "Answer 2.3" }}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 21 "P:=a*x^3+b*x^2+c*x+d;" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 40 "subs(x=0.01,a=-1/5,b=2/5,c=0,d=13/15,P);" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{SECT 1 {PARA 4 "" 0 "" {TEXT 330 12 "Exercise 2.4" }} {PARA 0 "" 0 "" {TEXT -1 8 "Use the " }{TEXT 331 7 "subs( )" }{TEXT -1 80 " command to check if any of the numbers: 1,2 or 3 is a solution to the equation:" }}{PARA 259 "" 0 "" {TEXT -1 1 " " }{XPPEDIT 18 0 " x^3-16*x^2+51*x-36=0" "6#/,**$%\"xG\"\"$\"\"\"*&\"#;F(*$F&\"\"#F(!\"\" *&\"#^F(F&F(F(\"#OF-\"\"!" }{TEXT -1 2 " " }}{SECT 1 {PARA 20 "" 0 " " {TEXT 328 21 "Student 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 20 "" 0 "" {TEXT 329 10 "Answer \+ 2.4" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "eqn:=x^3-16*x^2+51*x-36=0;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "subs(x=1,eqn);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "subs(x=2,eqn);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "subs(x=3,eqn);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 118 "Therefore x=1 and x=3 are solutions o f the equation. (In Section 5 you will learn how to solve equations us ing Maple.)" }}}}}{SECT 1 {PARA 4 "" 0 "expand( )" {TEXT -1 4 "The " }{TEXT 340 9 "expand( )" }{TEXT -1 8 " command" }}{PARA 0 "" 0 "" {TEXT -1 25 "The principal use of the " }{TEXT 278 10 "expand( ) " } {TEXT -1 144 "command is to \"multiply out\" products of polynomial ex pressions. 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 "Example 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',&*&\" \"$F&F%F&F&F*!\"\"F&,&F%F&\"\"&F&F&" }{TEXT -1 2 " ." }}{PARA 0 "" 0 " " {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "k:=(x+2)^2 *(3*x-3)*(x+5);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "expand(k );" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT 280 10 "Example 2:" }}{PARA 0 "" 0 "" {TEXT -1 63 "Maple applies some familiar trigonometric identities to expand " }{XPPEDIT 18 0 "si n(2*x)" "6#-%$sinG6#*&\"\"#\"\"\"%\"xGF(" }{TEXT -1 5 " and " } {XPPEDIT 18 0 "cos(2*x)" "6#-%$cosG6#*&\"\"#\"\"\"%\"xGF(" }{TEXT -1 2 " ." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "expand(sin(2*x));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "expand(cos(2*x));" }}} {PARA 0 "" 0 "" {TEXT -1 85 "Try expanding the sine and cosine of some other integer multiples of x. For example: " }{XPPEDIT 18 0 "sin(3*x) " "6#-%$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 example. 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(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 "Expand " }{XPPEDIT 18 0 "( x +1 )^n" "6#),&%\"xG\"\"\"F&F&%\"n G" }{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 "" }}}}{SECT 1 {PARA 20 "" 0 " " {TEXT 292 10 "Answer 2.6" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "expand((x+1)^2);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "exp and((x+1)^3);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "expand((x+ 1)^4);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}} {PARA 0 "" 0 "" {TEXT -1 0 "" }}}{SECT 1 {PARA 4 "" 0 "factor( )" {TEXT -1 4 "The " }{TEXT 341 9 "factor( )" }{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 "Exampl e 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$F%F%,&F'F%\"\"%F%F%" } {TEXT -1 19 " . Then apply the " }{TEXT 287 9 "factor( )" }{TEXT -1 107 " command to the result. Can you explain why the final result look s different than the original expression ?" }}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 31 "H:=2*(x-2)*(2*x^2+5*x+2)*(x+4);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "ans:=expand(H);" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 12 "factor(ans);" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT 264 10 "Example 3:" }}{PARA 0 "" 0 "" {TEXT -1 57 "Maple can factor expressions with more than one variable." }} {PARA 0 "" 0 "" {TEXT -1 25 "Factor the expression: " }{XPPEDIT 18 0 "x^2y+2xy+y" "6#,(*&%\"xG\"\"#%\"yG\"\"\"F(*&F&F(%#xyGF(F(F'F(" }} {PARA 11 "" 1 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "h:=x^2*y+2*x*y+y;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 " factor(h);" }}}{PARA 0 "" 0 "" {TEXT 265 10 "Example 4:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 125 "If Maple can't fact or an expression using rational numbers (i.e. integers and fractions) \+ then it returns the input unchanged." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "factor(3*x^2-10*x-9);" }}}{PARA 0 "" 0 "" {TEXT 267 10 "Example 5:" }}{PARA 0 "" 0 "" {TEXT -1 87 "The factor command is n ot limited to polynomials. It can be used to factor other forms." }} {PARA 0 "" 0 "" {TEXT -1 7 "Factor " }{XPPEDIT 18 0 "sin^2x -cos^2x: " "6#,&*&%$sinG\"\"#%\"xG\"\"\"F(*&%$cosGF&F'F(!\"\"" }{TEXT -1 2 " . " }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "factor((sin(x))^2-(cos(x )^2));" }}}{PARA 0 "" 0 "" {TEXT 268 10 "Example 6:" }}{PARA 0 "" 0 " " {TEXT -1 166 "If the factor command is used with a rational expressi on, the numerator and denominator are each factored and common factors are cancelled to simplify the expression:" }{MPLTEXT 1 0 0 "" }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "A:=(x^3-7*x^2+15*x-9)/(x^2+4 *x+4);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "factor(A);" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "B:=(x^3-7*x^2+15*x-9)/(x^2-4 *x+3);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "factor(B);" }}} {PARA 0 "" 0 "" {TEXT -1 74 "The next example allows you to see the fa ctored form without cancellation." }}{PARA 0 "" 0 "" {TEXT 349 10 "Exa mple 7:" }}{PARA 0 "" 0 "" {TEXT -1 8 "Maple's " }{TEXT 350 8 "numer( \+ )" }{TEXT -1 5 " and " }{TEXT 351 9 "denom( ) " }{TEXT -1 220 "command s allow you to isolate either the numerator or denominator of a fracti on. Here we use these commands to examine the factors of the numerator and denominator separately (i.e. before cancellation of common factor s)." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "B:=(x^3-7*x^2+15*x-9) /(x^2-4*x+3);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "factor(num er(B)); factor(denom(B));" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{SECT 1 {PARA 4 "" 0 "" {TEXT 259 12 "Exercise 2.8" }}{PARA 0 "" 0 "" {TEXT -1 22 "Factor the expression " }{XPPEDIT 18 0 "3x^4-2x^3+22x^2-18x-45 \+ " "6#,,*&\"\"$\"\"\"*$%\"xG\"\"%F&F&*&\"\"#F&*$F(F%F&!\"\"*&\"#AF&*$F( F+F&F&*&\"#=F&F(F&F-\"#XF-" }{TEXT -1 2 " ." }}{SECT 1 {PARA 20 "" 0 " " {TEXT 260 18 "Student Workspace " }{TEXT 343 3 "2.8" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 5 "" 0 "" {TEXT -1 7 " Answer " }{TEXT 344 3 "2.8" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "factor(3*x^4-2*x^3+22*x^2-18*x-45); " }}}}}{SECT 1 {PARA 4 "" 0 "" {TEXT 261 12 "Exercise 2.9" }}{PARA 0 " " 0 "" {TEXT -1 25 "Factor the expression " }{XPPEDIT 18 0 "x^(1/2) -x^(3/2" "6#,&)%\"xG*&\"\"\"F'\"\"#!\"\"F')F%*&\"\"$F'F(F)F)" }{TEXT -1 59 " and then use the expand command 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 5 "" 0 "" {TEXT -1 7 "Answer " }{TEXT 346 3 "2.9" }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "ww:=x^(1/2)-x^(3/2);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "factor(ww);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "expand(%); " }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}}}{SECT 1 {PARA 4 "" 0 "simplify ( )" {TEXT -1 4 "The " }{TEXT 342 11 "simplify( )" }{TEXT -1 8 " comm and" }}{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**$- F&6#F(F1F*F**&F1F**$-F-6#F(F1F*!\"\"-F&6#*&F1F*F(F*F9" }{TEXT -1 116 " . Maple can apply identities to simplify many lengthy mathematical ex pressions, such as trigonometric expressions. " }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 60 "V:=cos(x)^5 + sin(x)^4 + 2*cos(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 "Ex ample 2:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 137 "Trigonometric expressions with arguments in multiples of some ang le will be simplified to trig functions in the single angle if possibl e:" }}{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 expressions. " }}{PARA 0 "" 0 " " {TEXT -1 17 "Rewrite the sum " }{XPPEDIT 18 0 "1/(x+1)+x/(x-1)" "6# ,&*&\"\"\"F%,&%\"xGF%F%F%!\"\"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 "simpl ify(M);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{SECT 1 {PARA 4 "" 0 "" {TEXT 272 14 "Exercise 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) 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 5 "" 0 "" {TEXT -1 7 "Answer " }{TEXT 348 4 "2.11" }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "simplify(7/(x+2)+(3*x)/(x+2)^2);" }}}}}{SECT 1 {PARA 4 "" 0 "" {TEXT 274 13 "Exercise 2.12" }}{PARA 0 "" 0 "" {TEXT -1 24 "How does M aple simplify " }{XPPEDIT 18 0 "sin(3*t)-sin(7*t)" "6#,&-%$sinG6#*&\" \"$\"\"\"%\"tGF)F)-F%6#*&\"\"(F)F*F)!\"\"" }{TEXT -1 102 " ? Whether \+ or not this \"simplified\" form is of use to you will depend on what y ou 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 "" }}}}{SECT 1 {PARA 20 "" 0 "" {TEXT 276 11 "Answer 2.12" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "h:=sin(3* t)-sin(7*t);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "simplify(h) ;" }}}}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "1 0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }