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{SECT 0 {PARA 4 "" 0 "" {TEXT -1 0 "" }}{PARA 4 "" 0 "" {TEXT -1 18 "M
odule 1 : Algebra" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 3 "" 0 "" 
{TEXT -1 27 "102 : Simplify & Substitute" }}{PARA 0 "" 0 "" {TEXT -1 
0 "" }}{PARA 256 "" 0 "" {TEXT -1 17 "O B J E C T I V E" }}{PARA 0 "" 
0 "" {TEXT -1 267 "The objective of this module is to learn about vari
ables and some of the common algebraic operations that can be performe
d on an algebraic expression. We can simplify expressions, factor and \+
expand expressions, and substitute values for the variables in express
ions, " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "
" }}{PARA 4 "" 0 "" {TEXT -1 70 "_____________________________________
_________________________________" }}{PARA 4 "" 0 "" {TEXT -1 26 "A. V
ariables & Expressions" }}{PARA 0 "" 0 "" {TEXT -1 82 "_______________
___________________________________________________________________" }
}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
{PARA 0 "" 0 "" {TEXT -1 198 "In this section we'll learn about variab
les, expressions, and evaluation. In the previous module 201, we worke
d only with numbers. However, operations with variables can be perform
ed just as easily." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT -1 97 "Note that the remarkable in these expression are unknowns
 and are dealt with purely symbolically." }}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 31 " 3 + 4*x;    \011\011x^2;  \011\0111/(x-2);" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#,&\"\"$\"\"\"*&\"\"%F%%\"xGF%F%" }}{PARA 11 
"" 1 "" {XPPMATH 20 "6#*$)%\"xG\"\"#\"\"\"" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#*&\"\"\"F$,&%\"xGF$\"\"#!\"\"F(" }}}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 
-1 434 "Any meaningful combination of variables and numbers is an alge
braic expression. Remember that multiplication in Maple is accomplishe
d by using the * character, not juxtaposition as we normally do in mat
hematics. In other words, to write 5x2 + 7x, you would write 5*x^2 + 7
*x. One of the most common mistakes in Maple is to forget to use the s
tar for multiplication - for example, writing that last expression inc
orrectly as 5x^2 + 7x." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 
0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT -1 251 "A1  Write the following expressions in Maple            \+
 \n\011A. 1 - 2x                           \011\011B. 3x + 5y + 8    \+
\011                         C.    9x2 - 4    \n\011D. (2x \320 3)(4x \+
+ 5)   \011 (hint there are three multiplications occurring here)\n
\011E. 1/(x + 7)" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 
-1 244 "You can also define a variable to be equal to a certain value \+
using :=. In a sense, the variables become constants because Maple wil
l remember their values from that point on. Any expressions including \+
these values will be computed numerically." }}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 12 " a  := 29 ;\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%
\"aG\"#H" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "x :=  73.45;" }
}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"xG$\"%Xt!\"#" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 17 " a + x; a*x; a/x;" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#$\"&X-\"!\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"'0I@
!\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+DTE[R!#5" }}}{PARA 0 "" 0 
"" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 260 "Variable names in Map
le are not limited to single characters as commonly done in mathematic
s. Variable names can be more descriptive of the values they represent
. However they must begin with a character and must not include any bl
anks spaces within the name. " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 " gas_pressure  := 13.25;\n" 
}}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%-gas_pressureG$\"%D8!\"#" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "interest_rate :=  .08125;\n
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%.interest_rateG$\"%D\")!\"&" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "profit = revenue - cost;" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#/%'profitG,&%(revenueG\"\"\"%%costG!\"
\"" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 93 "Be
 careful, Maple is case sensitive. Maple makes a distinction between u
pper and lower case. " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 
"" {TEXT -1 120 "Be careful not to hit the shift key accidentally. In \+
the first example, the values of x and X are completely different! " }
}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 27 " x := 33;    X := 200;    \n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#
>%\"xG\"#L" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"XG\"$+#" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "x+x;   X+X;  x+X;\n" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#\"#m" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"$+%" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#\"$L#" }}}{PARA 0 "" 0 "" {TEXT -1 0 "
" }}{PARA 0 "" 0 "" {TEXT -1 149 "In the next example, Maple knows tha
t rate is 10, but does not recognize the new variable Rate. Rate and r
ate are treated as two different variables." }}{PARA 0 "" 0 "" {TEXT 
-1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "rate := 10; Rate +
 rate;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%rateG\"#5" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#,&%%RateG\"\"\"\"#5F%" }}}{PARA 0 "" 0 "" {TEXT 
-1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 112 "If you give a value to a varia
ble, Maple will remember it, and use it in any expression that uses th
at variable." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 19 "  a := 3;  b := 5;\n" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#>%\"aG\"\"$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"bG\"\"&" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "  a + b;  a^2 + b^2;" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\")" }}{PARA 11 "" 1 "" {XPPMATH 20 
"6#\"#M" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 
205 "The only drawback is that these letters are now associated with t
hose numbers. The only way to reset them to be indefinite variables ag
ain is to use the restart command or use the strange looking command :
" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 24 "  a := `a`;   b := `b`;\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>
%\"aG\"\"$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"bG\"\"&" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "a + b; a^2 + b^2;" }}{PARA 11 "" 1 
"" {XPPMATH 20 "6#\"\")" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"#M" }}}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 
0 "" 0 "" {TEXT -1 0 "" }}{PARA 4 "" 0 "" {TEXT -1 70 "_______________
_______________________________________________________" }}{PARA 4 "" 
0 "" {TEXT -1 22 "B. Substituting Values" }}{PARA 0 "" 0 "" {TEXT -1 
82 "__________________________________________________________________
________________" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 208 "A safer method of substi
tuting values for variables is to use the subs command. With this comm
and, you can replace variables in algebraic expressions, without perma
nantly changing the values of the variables." }}{PARA 0 "" 0 "" {TEXT 
-1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 " restart;\n" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 " subs( x = 19, x^7 - 31*x^6)
;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#!*s0bk&" }}}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 81 "You can also give a name \+
to an expression to make it more convenient to refer to." }}{PARA 0 "
" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 167 "Here, we define a
n expression and name it expr.\nWe substitute 5 for x in the expressio
n and find the result\nNext we evaluate at x=2 and x=0, and compute th
ose results." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 26 " expr:=(2*x + 1)/(5-3*x);\n" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%%exprG*&,&%\"xG\"\"#\"\"\"F)F),&\"\"&F)*&\"\"$F)F'F)!
\"\"F." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "subs( x = 5, expr
);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6##!#6\"#5" }}}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 21 " subs( x = 2, expr);\n" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#!\"&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "subs
( x = 0, expr);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6##\"\"\"\"\"&" }}}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 70 "You can e
ven substitute other variables or expressions for a variable." }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
30 " subs( x =  distance,  expr);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6
#*&,&%)distanceG\"\"#\"\"\"F'F',&\"\"&F'*&\"\"$F'F%F'!\"\"F," }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "subs( x =  a+3,      expr); \+
 \n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&,&%\"aG\"\"#\"\"(\"\"\"F(,&!
\"%F(*&\"\"$F(F%F(!\"\"F-" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
12 "simplify(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*&,&%\"aG\"\"#\"
\"(\"\"\"F),&\"\"%F)*&\"\"$F)F&F)F)!\"\"F." }}}{PARA 0 "" 0 "" {TEXT 
-1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 67 "You can also substitute into mu
ltivariable expressions at one time." }}{PARA 0 "" 0 "" {TEXT -1 0 "" 
}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 " expr:=(7*x  - 3)/(1 + x^2
 - y^2);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%exprG*&,&%\"xG\"\"(\"
\"$!\"\"\"\"\",(F+F+*$)F'\"\"#F+F+*$)%\"yGF/F+F*F*" }}}{EXCHG {PARA 0 
"> " 0 "" {MPLTEXT 1 0 29 "subs( \{x = 5, y = 2\}, expr);\n" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6##\"#;\"#6" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 29 " subs( \{x = A, y = B\}, expr);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#*&,&%\"AG\"\"(\"\"$!\"\"\"\"\",(F)F)*$)F%\"\"#F)F)*$)%
\"BGF-F)F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 " subs( \{x \+
= a+3, y = a-3\}, expr);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&,&%\"aG
\"\"(\"#=\"\"\"F(,(F(F(*$),&F%F(\"\"$F(\"\"#F(F(*$),&F%F(F-!\"\"F.F(F2
F2" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }
}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 4 "" 0 "" {TEXT -1 70 "________
______________________________________________________________" }}
{PARA 4 "" 0 "" {TEXT -1 21 "C. Factor Expressions" }}{PARA 0 "" 0 "" 
{TEXT -1 82 "_________________________________________________________
_________________________" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "
" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 50 "Recall that Maple \+
can factor numbers, into primes." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "ifactor(  1234567890 );" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#*,-%!G6#\"\"#\"\"\")-F%6#\"\"$F'F(-F%6
#\"\"&F(-F%6#\"%.QF(-F%6#\"%2OF(" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
{PARA 0 "" 0 "" {TEXT -1 54 "Just as easily, Maple can factor algebrai
c expressions" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 24 " factor( x^2 -7*x -12);\n" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#,(*$)%\"xG\"\"#\"\"\"F(*&\"\"(F(F&F(!\"\"\"#7F+" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "factor( x^3 - 4*x^2 -3*x + 1
2);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&,&%\"xG\"\"\"\"\"%!\"\"F&,&
*$)F%\"\"#F&F&\"\"$F(F&" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "
" 0 "" {TEXT -1 76 "Prime polynomials can't be factored using rational
 numbers even using Maple!" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "factor( x^2 -x + 5);\011" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#,(*$)%\"xG\"\"#\"\"\"F(F&!\"\"\"\"&F(" }}}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 412 "A slight
ly more sophisticated way of doing this, is to name an expression and \+
then factor it separately. For example,  is the expression a4b7c-3 + a
-4b6c-2. Its useful to apply a liberal does of parentheses to this exp
ression to make sure that the exponents and products come out as they \+
should. Since it would be easy to make a mistake, its a good idea to v
iew the original AND the factored form we are seeking." }}{PARA 0 "" 
0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 58 " expr :
= (a^4)*(b^7)*(c^(-3)) + (a^(-4))*(b^6)* (c^(-2)):\n" }}}{PARA 0 "" 0 
"" {TEXT -1 371 "                                                     \+
                                               The colon ( rather than
 semi-colon) allows the command to                                    \+
                                                                      \+
                                                                      \+
                          be executed " }}{PARA 0 "" 0 "" {TEXT -1 
149 "                  Factored expression                            \+
                       Note that we can see both the original and the \+
factored form!" }}{PARA 0 "" 0 "" {TEXT -1 20 " Original expression" }
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 " expr  = factor( expr );" }
}{PARA 11 "" 1 "" {XPPMATH 20 "6#/,&*&*&)%\"aG\"\"%\"\"\")%\"bG\"\"(F*
F**$)%\"cG\"\"$F*!\"\"F**&*$)F,\"\"'F*F**&F'F*)F0\"\"#F*F2F**&*&F5F*,&
*&)F(\"\")F*F,F*F*F0F*F*F**&F/F*F'F*F2" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 31 " expr := r^7 - 3*r^5 + 2*r^3 :\n" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 23 "expr  = factor( expr );" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#/,(*$)%\"rG\"\"(\"\"\"F)*&\"\"$F))F'\"\"&F)!\"\"*&\"\"#
F))F'F+F)F)**F1F),&F'F)F)F.F),&F'F)F)F)F),&*$)F'F0F)F)F0F.F)" }}}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 
0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 167 "C1. Factor eac
h of these polynomials (Hints : remember to use * for multiplication a
nd ^ for exponents, also help yourself to as many parentheses as you n
eed.)\n    A. " }{XPPEDIT 19 1 "3*x^2+8*x+5" "6#,(*&\"\"$\"\"\"*$%\"xG
\"\"#F&F&*&\"\")F&F(F&F&\"\"&F&" }{TEXT -1 50 "                       \+
                       B.  " }{XPPEDIT 19 1 "3*x^2+16*x+5;" "6#,(*&\"
\"$\"\"\"*$%\"xG\"\"#F&F&*&\"#;F&F(F&F&\"\"&F&" }{TEXT -1 40 "        \+
                            C.  " }{XPPEDIT 19 1 "x^4-3*x^2+2;" "6#,(*
$%\"xG\"\"%\"\"\"*&\"\"$F'*$F%\"\"#F'!\"\"F+F'" }}{PARA 0 "" 0 "" 
{TEXT -1 7 "    D. " }{XPPEDIT 19 1 "x^4-5*x^2+4;" "6#,(*$%\"xG\"\"%\"
\"\"*&\"\"&F'*$F%\"\"#F'!\"\"F&F'" }{TEXT -1 50 "                     \+
                         E.  " }{XPPEDIT 19 1 "24389*x^12-2197;" "6#,&
*&\"&*QC\"\"\"*$%\"xG\"#7F&F&\"%(>#!\"\"" }{TEXT -1 35 "              \+
                  F. " }{XPPEDIT 19 1 "36*a^13*b^10-40*a^11*b^11;" "6#
,&*(\"#O\"\"\"*$%\"aG\"#8F&%\"bG\"#5F&*(\"#SF&*$F(\"#6F&F*F/!\"\"" }
{TEXT -1 2 "  " }}{PARA 0 "" 0 "" {TEXT -1 7 "    G. " }{XPPEDIT 19 1 
"10*x^4-19*x^3+26*x^2-38*x+12;" "6#,,*&\"#5\"\"\"*$%\"xG\"\"%F&F&*&\"#
>F&*$F(\"\"$F&!\"\"*&\"#EF&*$F(\"\"#F&F&*&\"#QF&F(F&F.\"#7F&" }{TEXT 
-1 45 "                                         H.  " }{XPPEDIT 19 1 "
x^5+9*x^4*y-10*x^3*y^2-186*x^2*y*3+9*x*y^4+945*y^5;" "6#,.*$%\"xG\"\"&
\"\"\"*(\"\"*F'*$F%\"\"%F'%\"yGF'F'*(\"#5F'*$F%\"\"$F'F,\"\"#!\"\"**\"
$'=F'*$F%F1F'F,F'F0F'F2*(F)F'F%F'F,F+F'*&\"$X*F'*$F,F&F'F'" }}{PARA 0 
"" 0 "" {TEXT -1 4 "    " }}{PARA 4 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "
" 0 "" {TEXT -1 0 "" }}{PARA 4 "" 0 "" {TEXT -1 70 "__________________
____________________________________________________" }}{PARA 4 "" 0 "
" {TEXT -1 24 "D. Expanding Expressions" }}{PARA 0 "" 0 "" {TEXT -1 
82 "__________________________________________________________________
________________" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 136 "Maple can operate in bot
h directions - factoring expressions (taking them apart) and expanding
 expressions (putting them back together)." }}{PARA 0 "" 0 "" {TEXT 
-1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 81 "If we raise an expression to a \+
power, Maple returns the same expression verbatim." }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 " (x - 2) ^ 1
0; " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*$),&%\"xG\"\"\"\"\"#!\"\"\"#5F
'" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 93 "If \+
we want to actually multiply the powers out and see the result, we use
 the expand command." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 25 " expand(  (x - 2) ^ 10 );" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#,8*$)%\"xG\"#5\"\"\"F(*&\"#?F()F&\"\"*F(!\"\"*&\"$
!=F()F&\"\")F(F(*&\"$g*F()F&\"\"(F(F-*&\"%gLF()F&\"\"'F(F(*&\"%k!)F()F
&\"\"&F(F-*&\"&SM\"F()F&\"\"%F(F(*&\"&g`\"F()F&\"\"$F(F-*&\"&?:\"F()F&
\"\"#F(F(*&\"%?^F(F&F(F-\"%C5F(" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
{PARA 0 "" 0 "" {TEXT -1 113 "You could do this by hand, but it would \+
take a long time! Here is a slightly more sophisticated way of doing i
t :" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 34 " (a - 2*b) ^ 10;    % = expand(%);" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#*$),&%\"aG\"\"\"*&\"\"#F'%\"bGF'!\"\"\"#5F'" }}{PARA 
12 "" 1 "" {XPPMATH 20 "6#/*$),&%\"aG\"\"\"*&\"\"#F(%\"bGF(!\"\"\"#5F(
,8*$)F'F-F(F(*(\"#?F()F'\"\"*F(F+F(F,*(\"$!=F()F'\"\")F()F+F*F(F(*(\"$
g*F()F'\"\"(F()F+\"\"$F(F,*(\"%gLF()F'\"\"'F()F+\"\"%F(F(*(\"%k!)F()F'
\"\"&F()F+FIF(F,*(\"&SM\"F()F'FEF()F+FCF(F(*(\"&g`\"F()F'F?F()F+F=F(F,
*(\"&?:\"F()F'F*F()F+F8F(F(*(\"%?^F(F'F()F+F4F(F,*&\"%C5F()F+F-F(F(" }
}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 29 "D1. Expan
d these expressions\n" }}{PARA 0 "" 0 "" {TEXT -1 69 "      A. (5x - 1
)^13   \011B. (x^2 + x + 1)10    C. (x-2)(x+3)(x-4)(x+5)" }}{PARA 0 "
" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "
" {TEXT -1 0 "" }}{PARA 4 "" 0 "" {TEXT -1 70 "_______________________
_______________________________________________" }}{PARA 4 "" 0 "" 
{TEXT -1 26 "E. Simplifying Expressions" }}{PARA 0 "" 0 "" {TEXT -1 
82 "__________________________________________________________________
________________" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 129 "Many of the problems in \+
algebra involve simplifying expressions. Maple will automatically simp
lify some that are relatively easy." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 " 3*(x-1) + 7*(x+2) - 5*(x+1
1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&%\"xG\"\"&\"#W!\"\"" }}}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 70 "However, \+
more complicated expressions will not simplify automatically." }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
37 " 3*(x-1)^2 + 7*(x+2)^3 - 5*(x+11)^4; " }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#,(*$),&%\"xG\"\"\"F(!\"\"\"\"#F(\"\"$*&\"\"(F(),&F'F(F*
F(F+F(F(*&\"\"&F(),&F'F(\"#6F(\"\"%F(F)" }}}{PARA 0 "" 0 "" {TEXT -1 
0 "" }}{PARA 0 "" 0 "" {TEXT -1 63 "We need to tell Maple that we want
 to simplify this expression." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 " simplify(%);" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6#,,*$)%\"xG\"\"#\"\"\"!%&e$*&\"&Ul#F(F&F(!\"\"\"&
YJ(F,*&\"$8#F()F&\"\"$F(F,*&\"\"&F()F&\"\"%F(F," }}}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 54 "Maple can also simplify r
ational and root expressions." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 " 7/(x-3) + 4/(x+5):       % \+
= simplify( % );\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/,&*&\"\"\"F&,&%
\"xGF&\"\"$!\"\"F*\"\"(*&\"\"%F&,&F(F&\"\"&F&F*F&*&,&F(\"#6\"#BF&F&*&F
'F&F.F&F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "sqrt(x+3) - 2/
sqrt(x+3):  % = simplify(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/,&*$-
%%sqrtG6#,&%\"xG\"\"\"\"\"$F+F+F+*&\"\"#F+*$-F'6#F)F+!\"\"F2*&,&F*F+F+
F+F+*$-F'6#F)F+F2" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 
-1 18 "E1.  Simplify\n    " }}{PARA 0 "" 0 "" {TEXT -1 85 "     A.  1/
(x^2 + 19*x + 90) + 1/(x^2 - 81)         B. 4*(2*x+9)^2 - 5*(8-x)^2   \+
    " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}}}{MARK "1 0" 6 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 
}{PAGENUMBERS 0 1 2 33 1 1 }