' +JJJJ ?\>m0M='+l> /+l   d]@ŵLҦ]]L L}BBL]렮 鷎귭෍ᷩ췩緈JJJJx Lȿ L8ᷭ緍췩 緍i 8 `巬 췌`x (`(8`I`B` ``>J>J>VU)?`8'x0|&HhHh VY)'&Y)xꪽ)' `Hh`V0^*^*>&` aI꽌ɪVɭ&Y&&Y& 꽌ɪ\8`&&꽌ɪɖ'*&%&,E'зЮ꽌ɪ`+*xS&x'8*3Ixix&& 8  '  & x)*++`FG8`0($ p,&"_]` L/浍굺L  !"#$%&'()*+,-./0123456789:;<=>?  1#"""  (9"1 ( ,.(0# 2  /#0/#0 *?'#07#00/0/'#07#0:"4<*55/**5/*%5/)1/)1/)1/)'#0/#0*5/*75/**5/*:5//#0/#0'#07#0:::*::'#07#0EB H  @H !D)"E` @ $ C ` DQ &J80^݌Hh ü ü݌ ռ ռ ռA ļD ļ? ļAEDE?HJ>h Լ ռ ռ ռ`HJ>݌h Hh݌`HIHHHHhHH݌hHhHh݌H6 VDP (ED Z $0x8x D- ܸDD# H8`?E Vk *f???0xE Hh D#-EEE8` D ܸx D - ܸx8`-0ݩ?ʥD EEE`   vLDcpq` [` ~  LӜu`".Q`pNФbptťܥm2<(-Py0\|e<6e<g< JJJJj귍hI  aUL@ kU8  L  Q^R(jQ0l^l\  wUuW ԧ H h@ [_ /QSIRb_L`LLLL`ª`LQLYLeLXLeLee ўQH\(h0L& Ꝥ$`( R \ZLl8 ўR HH\`\Z[YS6`LxQɿu3'RͲʎRʎ]]]ɍuL͟ɍ}RLRɍg^H8 ^hZLɍR LͲɊRR% QLܤͲ Z@ -^ ş\[Z QY\[Z8`l6Lş_Ȍb_Ͳ] )Y h( ֭ͲLɍ [LLĦ__ ^ 9 LҦ3 9 a   0LjLY u< (_9 ˭ɠuɠK_9 ?LˆʎõĵL õ ĵµ aµ`` L̦µ_bJLuLz`  ȟ QlXJ̥KlV  ȟ QlV eօ3L e3L &RL &QL d L4 Ne)n `@-eff L f`L . tQLѤ LҦL` OPu d L Ne)noon 8ɍ` ^f\õL ^NR  RΩLҦ)\Z ʽ LHv 3h`0h8` [L NС õ`A@` ŵL^L iõ`  \ 濭0 \  ȟ Q ^\lZl^?cqH şch`fhjõĵ@OAP`u@`@&`QR`E Ls  @DAE@u`8` %@ @A@`@`@A`Mµ ) LЦ`8@AWc@8@-@HAȑ@hHȑ@ȑ@hHȑ@Ȋ@ch8&ȑ@Hȑ@Ah@LHȑ@ȑ@ htphso`hMhL`9V8U897T6S67`INILOASAVRUCHAIDELETLOCUNLOCCLOSREAEXEWRITPOSITIOOPEAPPENRENAMCATALOMONOMOPRINMAXFILEFINBSAVBLOABRUVERIF!pppp p p p p`" t""#x"p0p@p@@@p@!y q q p@  LANGUAGE NOT AVAILABLRANGE ERROWRITE PROTECTEEND OF DATFILE NOT FOUNVOLUME MISMATCI/O ERRODISK FULFILE LOCKESYNTAX ERRONO BUFFERS AVAILABLFILE TYPE MISMATCPROGRAM TOO LARGNOT DIRECT COMMANč$3>L[dmxӜ ( \ Ϡ@跻~!Wo*9~~~~ɬƬ~_ j ʪHɪH`Lc (L ܫ㵮赎 ɱ^_ J QL_Ls贩紎 DǴҵԵƴѵӵµȴ 7 ַ :ŵƴѵǴҵȴµ納贍﵎ٵ്ᵭⳍڵL^ѵ-I `  4 ò-յ!  8صٵ紭ﵝ 7L (0+BC  7L HH`LgL{0 HH` õL H hBL BH [ h`Lo õ ڬL B ڬ LʬH hB@ յյ [L (ȴ) ȴ 7L L ( L (ȴL{ƴѵ洩ƴǴҵ 7 ^* B0 HȱBh ӵԵ 8 L8 ݲ` ܫ  / / ED B / / ]ƴS0Jȴ ȴ)  紅D贅E B ƴ  / 0L Ν `HD٤DEEhiHLGh ` ŵBѵ-` ѵB-` ܫ XI볩쳢8 DH E𳈈췍Ȍ X0 · JLǵBȵC`,յp` 䯩 R-յյ`յ0` K R-յյ`ɵʵӵԵ` 4 K ( ѵҵLBȱBL8` DBHBH : ַ޵BȭߵBhhӵԵ RBܵmڵ޵ȱBݵm۵ߵ` 䯩LR˵̵ֵ׵`êĪLR E( 8` R` ELRŪƪ`췌 յյI뷭鷭귭ⵍ㵍跬ª 뷰` Lf ݵܵߵ޵ ^`8ܵ i B8` 4L ֵȱB׵ ܯ䵍൭嵍 ` DȑB׵Bֵ  ַ յյ`굎뵎쵬 뵎쵌``õĵBCõĵ`µµ`L õBĵCصص Qƴ0"Bƴ 󮜳` 0۰ϬBƴ8`i#`ЗLw!0>ﵭ` m ﳐ 7i볍 8 ЉLw`H h ݲL~ `浍국䵍뵩嵠Jm赍嵊mjnnn浈m浍浭m䵍䵐`"L ŵ8ŵH ~(` d ֠z#ILoLHllLŌŒlaHŒ\LŒ\KH\HLHlaH\朻\\LŒ\\HFlHHHHCHlaClLŒ\霿gLŒ\Č,[ELOL` u`(*A*@ T  ``}ǟĈq`W*]jU~(*A*@ T 0`|L?xC3@~ F`ծ`p`d`*]jWD0`0Na f03@ g0D*A T  `ծ``ϼѿ|`/}zD0`0Oaf~3@LgD*A T  `׾`~o}ת}`~_{/Uz`Ğ`D 0f0XMaxcsOlfA `׿ժu`z/j+Uj`虢`D 0o0xLa `3X˭ZZ0ĭZH90ZHZH32Z@˭ZZ0ĭZH97ZHZH32C˺(ZH);:ZZZZ1:N$N$(ZH):52025H˭ZZ052025ȍM˺(8)" "(8);:ZZ1G$"":G1$"":N$"":ZZ0:52025NN$(N$,(N$)1):ZZZZ1:52025ϲ INIT MESSAGE6);:::" Please enter your first name (up to"::" ten letters) and press .":::10)"Name: ";4ZZ0:N$"":G1$"":ZH0Ռ9˾G1$:G1$(8)52025:XX((78)(79))16:XX(XX):ZH(G1$):ZH13ZZ0ı:˭ZH852040;˭ZZ1052025<˭ZH Workshops":17:15:"Courseware":19:17:"@ 1984"ú(9);:ZZ140:1:ZZ:" ";:23:ZZ:" ";::ZZ122:ZZ:1:" ";:40:" ";::(14);ÁZZ12500:ZZ:8DzLOAD/INIT SHAPE TABLE`Ǻ(13);(4);"BLOAD SHAPES":232,0:233,3: ˲NAMEj*˺(1::"completely.":12000R(16):12:12:"Enjoy the problems!":ZZ13000:ZZ:]PòTITLEuZÑ:16302,0:(1);1Ċdâ7:9:"Binomial Multiplication":10:5:"By Mark Berman and Kevin Vessio"2xâ12:11:"Designed by Don Ross":15:9:"Microcomputerle terms will cancel, but in"::"other problems (like the first practice"::"problem), there will be no like terms.":1200016000:" However, in most cases, you will be"::"able to combine like terms, although"::"they may not cancel each other"20b11:19:"x~-49":16000:"Excellent, ";N$;"."::" Notice that in this problem, the sum":"of the like terms is zero, so the middle":"two terms dropped out completely.":12000| 16000:" In a few problems (like this one),"::"the middVT%:HF%,VT%HF%,VB%HS%,VB%HS%,VT%:12000:V2%1:1:80)؟H30:16000:"Enter sum of the like terms: ";:13000:Z$G$:Z$""40920ݟ31000:Z$"0"Z$"-0"Z$"+0"40950⟖1:18:"That's not the correct sum, ";N$;"."::"-7x + 7x = 0":12000:409ğ16000:" Here's the twist. In this product,"::"the second and third terms are like"::"terms. To get the final answer, you"::"must simplify by combining like terms.":ΟVT%8V2%3:VB%VT%10:HF%7H2%17.5:HS%HF%21:3:16:1HF%,VT%:1HS%,,2)7:VA$(2,2)"":10000:V2%8:H2%16:V2%:H2%:"x~"ᅈ16000:" I've started you off on this problem"::"by filling in the product of the first"::"terms. Now you try doing the rest of"::"the FOIL sequence.":12000I24:PA%I:15000:Iost of the work, but I'll help"::"at the end. (This problem has a little"::"twist to it.)":12000:2:1:(6):12:"________________________________________"5~VP%5:HP%16:CO%(1,1)1:VA$(1,1)"x":CO%(1,2)7:VA$(1,2)"":CO%(2,1)1:VA$(2,1)"x":CO%(2ve and commutative laws.":12000`(16);4);"The FOIL method: Extra practice":1:5:(15);(15);"________________________________";(15);(16):j" Before you start to work on problems,":"let's try one more example. You'll have"t"to do mibutive":-L"and commutative laws.":12000Q16000:" Since we can distribute and commute"::"with any binomials, we know that FOIL":V"can be used whenever we multiply two"::"binomials. FOIL is just a shortcut for":["the distributi1x ":10:14ZZ:" - 2xy":QQ1150:QQ,ZZh.8:15:5);:9:15:"+ 21x":10:21:5);:9:21:"- 2xy"811:13:"Outside Inside":112,80119,73:182,80168,73 B16000:" Now you can see that FOIL gives the"::"same result as using the distr into FOIL."y11:4:"First Inside Outside Last":3:40,8077,73:112,80119,73:182,80168,73:231,80210,731200010:13:17);:11:13:19);:9:15:11);)10:15:"- 2xy":8:21:"+ 21x":QQ1150:QQ:ZZ16:8:21ZZ:"+ 2lt. Does it seem familiar?":12000ޞ16000:" It should look very familiar. It's"::"the same result we found with FOIL,":螺"except that the second and third terms"::"have been exchanged. We can use the": "commutative law to turn FIOLable pieces. The only thing left"::"to do is the multiplication.":12000n~9:11:"3x~ - 2xy + 21x - 14y"~ʞ16000:" That's it, ";N$;". We have"::"multiplied two binomials, using the":"Ԟ"distributive law. Look carefully at"::"the resu:12000c}16000:" Now we use the distributive law"::"again on each of the two parts.":12000}7:5:"[(3x*x)+(-2y*x)]+[(3x*7)+(-2y*7)]"}16000:" By using the distributive law, we"::"have broken the original problem into":J~"manage_______________________"o|\14:" The first step is to use the"::"distributive law to split the product":|f"into two parts.":12000|p5:8:"(3x-2y)(x) + (3x-2y)(7)"}z16000:" Notice that I have distributed"::"(3x-2y) over (x+7)."uld also":{H"understand ";(1);"2why";(1);"1 the FOIL method works."::"Let's take another look at the problem"::"we just finished to see if we can find"::"out what makes FOIL work.":12000|R3:1:(6):VP%3:10000:12:1:"_________________roduct of (3x-2y) and (x+7) is"::"3x~+21x-2xy-14y.":12000z4(16);5);"The FOIL method: Why it works":1:5);(15);(15);"______________________________";(15);(16) {>3:1:" Now that you know how to multiply"::"binomials with FOIL, you sho:11000:15000yl16000:" By adding -14y to the sum, we have"::"finished all four letters of FOIL. Now"::"we try to simplify the product.":12000;zv16000:" Since the product has no pairs of"::"like terms, it can't be simplified. The":"pishing the problem."::"We're up to the third letter in FOIL.":12000:PA%3:ER%0:11000:15000 yD16000:"Good work, ";N$;"."::" Notice that I've added -2xy to the"::"other two terms. All we have left are"::"the last terms.":12000:PA%4:ER%0ond letter in FOIL is O. The"::"product of the outside terms (3x and 7)"::"is 21x.":12000w16000:" Continue to build the answer by"::"adding 21x to 3x~."w7:1:120);:8:13:"3x~+21x":12000:ER%1:11000_x:16000:" Now you try fin"put 3x~ on the next line as the first"::"term in the solution."vV2%8:H2%13:PA%1:14000:VA$PR$:CO%PR%:10500:V2%:H2%:RE$:C1$"2 1234 5 6781":V2%1:H2%1:C1$v12000:ER%1:11000:ER%0:PA%2:11000v16000^w" The sec ";N$;", let's try an"::"example. I'll start it off.":12000:16000u֜" The first letter in FOIL is F, so I"::"begin by multiplying the first term of"::"each binomial.":PA%1:11000:12000Av16000:" The product of 3x and x is 3x~. I"::s to"::"get the answer."'tr16368,0?t|12000:2:1:(6);tVP%5:HP%15:CO%(1,1)3:VA$(1,1)"x":CO%(1,2)2:VA$(1,2)"y":CO%(2,1)1:VA$(2,1)"x":CO%(2,2)7:VA$(2,2)"":10000t12:1:"________________________________________"Eu"All right,ds for: I nside":16:"L ast"sh12:" FOIL helps you remember to take the"::"products of the first, outside, inside,"::"and last terms of the two binomials."::"After you complete the multiplication,"::"you just add";ti" the four productrialvrJ(16);4);"The FOIL method: How to use it":1:4);(15);(15);"_______________________________";(15);(16)rT3:1:" The FOIL method is a technique for"::"multiplying binomials. The word FOIL":s^16:"F irst":16:"O utside":"stan""=qyZZ1(Z$):Z1$(Z$,ZZ,1):Z1$"1"ZZ$ZZ$Z1$:31160MqyZZ131150qy(Z$,ZZ1,1)"0"(Z$,ZZ1,1)"9"(Z$,ZZ1,1)"0"(Z$,ZZ1,1)"9"ZZ$ZZ$Z1$qy31160qy(Z$,2,1)"0"(Z$,2,1)"9"ZZ$ZZ$Z1$qyZZqyZ$ZZ$:r@Tuto2)(C1$,1)((C1$,2),1):CZZ$C2$)pvu;pyPREP STRINGSp,yZZ$"":ZZ1(Z$):Z1$(Z$,ZZ,1):Z1$" "Z1$"("Z1$")"Z1$"+"31050p6y(Z1$)64(Z1$)91Z1$((Z1$)32)p@yZZ$ZZ$Z1$pJyZZpTyZ$ZZ$p^yZ$"-1"31170:Z$"1"31170q|yZZ$,2)ZZ:7odCO%(2,1)CO%(2,1)ZZ:CO%(2,2)CO%(2,2)ZZ:Eo0uCOMP $'SXo:uC1$C2$C1:qoDuC1$""C2$""C0:oNuZ$C1$:31000:C1$Z$oXuZ$C2$:31000:C2$Z$obuCC1$C2$(C1$,1)"0"(C2$,1)"0"(C1$)0(C2$)0#pluC(C1$)2ZZ$(C1$,(C1$)(ZZCO%(1,1))7(ZZCO%(1,2))725700_nndR(2)2CO%(1,1)CO%(1,1)ZZ:CO%(1,2)CO%(1,2)ZZ:nxdCO%(2,1)CO%(2,1)ZZ:CO%(2,2)CO%(2,2)ZZ:nd25600:ZZR(2)1:(ZZCO%(1,1))7(ZZCO%(1,2))725800odR(2)2CO%(1,1)CO%(1,1)ZZ:CO%(1,2)CO%(1CO%(1,2)SIGN(0)R(7):VA$(1,2)(VAR(0)):CO%(2,1)CO%(1,1):VA$(2,1)VA$(1,1):CO%(2,2)CO%(1,2):VA$(2,2)VA$(1,2)m dVA$(1,1)VA$(1,2)25600mdZZ25:CO%(1,1)ZZ(CO%(1,1)ZZ)CO%(1,2)ZZ(CO%(1,2)ZZ)25600mdZZm(d&ndd25510:ZZR(2)1:(VAR(0)):CO%(1,2)SIGN(0)R(7):VA$(1,2)"":CO%(2,1)CO%(1,1):VA$(2,1)VA$(1,1):CO%(2,2)CO%(1,2):VA$(2,2)VA$(1,2)lcZZ25:CO%(1,1)ZZ(CO%(1,1)ZZ)CO%(1,2)ZZ(CO%(1,2)ZZ)25510lcZZlcsmdCO%(1,1)SIGN(0)R(7):VA$(1,1)(VAR(0)):R(7):VA$(2,1)(VAR(0)):CO%(2,2)SIGN(0)R(7):VA$(2,2)""ZkBcVA$(1,1)VA$(2,1)25400zkLc(2)1VA$(1,2)VA$(2,1):kVcVA$(2,2)VA$(1,1):kcR(10)25510,25600,25700,25800,25510,25600,25700,25800,25510,25600wlcCO%(1,1)SIGN(0)R(7):VA$(1,1)0)):CO%(1,2)SIGN(0)R(7):VA$(1,2)"":CO%(2,1)SIGN(0)R(7):VA$(2,1)(VAR(0)):CO%(2,2)SIGN(0)R(7):VA$(2,2)""jbVA$(1,1)VA$(2,1)25310jb=k8cCO%(1,1)SIGN(0)R(7):VA$(1,1)(VAR(0)):CO%(1,2)SIGN(0)R(7):VA$(1,2)"":CO%(2,1)SIGN(0)SIGN(0)R(7):VA$(1,2)(VAR(0)):CO%(2,1)SIGN(0)R(7):VA$(2,1)VA$(1,1):CO%(2,2)SIGN(0)R(7):VA$(2,2)VA$(1,2)izbCO%(1,1)CO%(2,2)CO%(1,2)CO%(2,1)0VA$(1,1)VA$(1,2)25200ibibR(2)225400vjbCO%(1,1)SIGN(0)R(7):VA$(1,1)(VAR(R(7):VA$(1,1)(VAR(0)):CO%(1,2)SIGN(0)R(7):VA$(1,2)"":CO%(2,1)SIGN(0)R(7):VA$(2,1)VA$(1,1):CO%(2,2)SIGN(0)R(7):VA$(2,2)VA$(1,2)h bCO%(1,1)CO%(2,2)CO%(1,2)CO%(2,1)025110h*bvipbCO%(1,1)SIGN(0)R(7):VA$(1,1)(VAR(0)):CO%(1,2)""ıgR(G$)2ı4gR(G$,2)"zx"Z$"xz":21100UgR(G$,2)"zy"Z$"yz":21100vgR(G$,2)"yx"Z$"xy":21100|g&RglR(G$)2G$Z$:gvRG$(G$,(G$)2)Z$:gaCREATE PROBgaR(10)25300,25500g bR(8)525200hbCO%(1,1)SIGN(0)0);:fPG$""LT%C1:?fP(G$""LT%)(G$""LT%)C0:qf P(G$)1(G$,1)"1"(G$)1G$(G$,(G$)1)f!P(G$)1(G$,2)"+1"(G$)2G$(G$,(G$)2)f#P(G$)1(G$,2)"-1"(G$)2G$"-"(G$,(G$)2)f(P21000:C2$G$:30000:gRG$$))2):TM$;:20400Ve~OPA%2:14000:CO%PR%:VA$PR$:10500:TM$RE$:(C1$,1)"0"20380ueO(C1$,1)"-"TM$TM$"+"eOTM$TM$C1$eOPA%3:14000:CO%PR%:VA$PR$:10500:(RE$,1)"-"TM$TM$"+"eOTM$TM$RE$:((41(TM$))2)TM$;fOV2%1:1:800dLOLT%20400.dVO11:TM$"":LT%120350rd`OPA%1:14000:CO%PR%:VA$PR$:10500:TM$RE$:(C1$,1)"0"20335deO(C1$,1)"-"TM$TM$"+"djOTM$TM$C1$doOPA%4:14000:CO%PR%:VA$PR$:10500:(RE$,1)"-"TM$TM$"+"etOTM$TM$RE$:((41(TMPA%3:14000:T1%T1%PR%:CO%PR%:10500:RE$;" = ";:CO%T1%:10500:RE$:12000:20200dO20:1:"Sorry, ";N$;"."::PA%1:14000:T1%PR%:CO%PR%:VA$PR$:10500:RE$;" + ";:PA%4:14000:T1%T1%PR%:CO%PR%:10500:RE$;" = ";:CO%T1%:10500:RE$:12000:2020:20500:C20300bNE2E21bNLT%Ģ18:1:"You can't combine any terms, ";N$;".":20:"None of the terms in the product are"::"like terms.":12000:20200TcOLT%1Ģ20:1:"Sorry, ";N$;"."::PA%2:14000:T1%PR%:CO%PR%:VA$PR$:10500:RE$;" + ";:E$):PA%1:14000:VA$PR$:CO%PR%:10500:HF%7(H2%1)3.5(RE$)aN1:16:3:1HF%,VT%:1HS%,VT%:HF%,VT%HF%,VB%HS%,VB%HS%,VT%aN12000bN16000:16:"Press RETURN if there are no like terms.":14:"Enter sum of like terms: ";:V14:H27:1300$:CO%PR%:10500:T1%7(H2%(RE$)):PA%2:14000:VA$PR$:CO%(PR%):10500:HF%T1%3.5(RE$):T1%T1%7(RE$)7:PA%3:14000:VA$PR$:CO%(PR%):10500:HS%T1%3.5(RE$)?aNLT%1T1%T1%7(RE$)7:PA%4:14000:VA$PR$:CO%(PR%):10500:HS%T1%3.5(R"of like terms.":20150_NLT%Ģ20:1:"That is incorrect, ";N$;". There"::"are no like terms in the product.":12000:20200_N20:1:"Not quite, ";N$;". You have made"::"an error in addition."_NVT%8V2%3:VB%VT%10`NPA%1:14000:VA$PR1)CO%(2,1)CO%(1,2)CO%(2,2):10500:C1$RE$6^zN12000^N16000:16:"Press RETURN if there are no like terms.":14:"Enter sum of like terms: ";:V14:H27:13000:20500:C20300^NE2E21_NLT%G$""Ģ20:1:"Sorry, ";N$;", there is a pair"::oduct by combining"::"any like terms."]RNLT%0:VA$(1,1)VA$(2,1)VA$(1,2)VA$(2,2)LT%1:PA%2:14000:VA$PR$:CO%CO%(1,1)CO%(2,2)CO%(1,2)CO%(2,1):10500:C1$RE$:20090+^\NVA$(1,2)VA$(2,1)VA$(1,1)VA$(2,2)LT%1:PA%1:14000:VA$PR$:CO%CO%(1,0"G$8\rBXX1(G$):(G$,XX,1)"."17020::G$G$".00"R\|BXX(G$)1G$G$"0"d\BG$(G$,XX2)w\B6(G$))G$:\ NCOMB LIKE TERMS\*N16000:"Good work, ";N$;". You have"::"finished the multiplication. Now you":']4N"must simplify the pr1T1%H2%:15540u[CLEAR MESSAGE[>13:1:(22);(16);(25);:14:1[>[hB DISPLAY #/2DEC PLACES\mBG$(Z):(G$,1)"."G$"y, ";N$;".":(Z;PA%2CO%(1,2)0ĺ"-";cZ;PR$(1(PA%2));" * ";:(PA%2PA%4)CO%(2,2)0ĺ"-";Z;PR$(3(PA%2(PA%2)));" = ";C2$Z;12000:16000:15200ZQf+1HF%,VB%:1HS%,VB%cQp+HF%,VB%HF%,VT%HS%,VT%HS%,VB%iQz+uQ.RETURNQ.16368,0:24:9:"Press RETURN to continue.";Q.ZZ(1):ZZ(16384):ZZ14112020Q.16368,0:24:7:30);:R2 GET ROUT$(CO%)VA$:P* POINT5P+VB%8VP%10:VT%VB%10_P +PA%3HF%7HP%3.5(PR$(1)):11040P+HF%7(HP%(PR$(1))1)3.5(PR$(2))P +PA%1PA%3HS%7(HP%(PR$(1))(PR$(2))3)3.5(PR$(3)):11100Q*+HS%7(HP%(PR$(1))(PR$(2))4(PR$(3)10500:PR$(4)RE$COB'VP%:HP%:"(";PR$(1);:CO%(1,2)0ĺ"-";:10070MOL'"+";OV'PR$(2);")(";PR$(3);:CO%(2,2)0ĺ"-";:10090O`'"+";Oj'PR$(4);")":O)VA$""RE$(CO%):O)CO%1RE$VA$:O)CO%1RE$"-"VA$:O)CO%0RE$"0": P")REb, ";N$;"."::"You're done with this problem.";Np12000:IN' DISPLAYyN'CO%CO%(1,1):VA$VA$(1,1):10500:PR$(1)RE$N$'CO%(CO%(1,2)):VA$VA$(1,2):10500:PR$(2)RE$N.'CO%CO%(2,1):VA$VA$(2,1):10500:PR$(3)RE$O8'CO%(CO%(2,2)):VA$VA$(2,2)::14000:VA$PR$:CO%CO%(1,1)CO%(2,1)CO%(1,2)CO%(2,2):10500:H3%H3%(RE$)(CO%0)((RE$)CO%0):PA%2:14000:VA$PR$:CO%PR%:10500:H3%H3%(RE$)MRPA%3:14000:VA$PR$:CO%PR%:10500:H3%H3%(RE$)(CO%0):H3%H3%2M\20000.Nf16000:"Nice jo41:PA%2:14000:VA$PR$:CO%CO%(1,2)CO%(2,1)CO%(1,1)CO%(2,2):10500:H3%H3%(RE$)(CO%0)((RE$)CO%0):PA%1:14000:VA$PR$:CO%PR%:10500:H3%H3%(RE$)L>PA%4:14000:VA$PR$:CO%PR%:10500:H3%H3%(RE$)(CO%0):H3%H3%2:2140MHH3%41:PA%1_____";K V2%8:H2%41:I14:PA%I:14000:CO%PR%:VA$PR$:10500:H2%H2%(RE$)(I1CO%0):I:H2%H2%2:I14:PA%I:15000:IKV3%11:VA$(1,1)VA$(2,1)VA$(1,2)VA$(2,2)2100K VA$(1,2)VA$(2,1)VA$(1,1)VA$(2,2)2120K*H3%H2%:2140L4H3%;"Problem #";P;:15:(15);(15);"__________";(15);(16);:P9ĺ(15);(15);"_";(15);(16);JVP%5:HP%37:I12:J12:CO%CO%(I,J):VA$VA$(I,J):10500:HP%HP%(RE$)(J2CO%0):J,I:HP%HP%2:10000K12:1:"___________________________________ ";:G$(E3E4):3(G$))G$;:Z(E3E4)P:34:17000:nI21:9:"You completed "P" problem";:P1ĺ".":1570xI"s."I"24:10:"Press "(9)"RETURN"(14)" for Menu.";:12020I@E10:E20:E30::200IPROBLEMIE10:E20:25000\J(16);14)(15);(15);"_____";:24:"______";:34:"_______";(15);(16);H11:"Multiplying Terms ..... ";:G$(E3):3(G$))G$;:ZE3P:34:17000:H13:"Combining Like Terms .. ";:G$(E4):3(G$))G$;:ZE4P:34:17000:5I17:"Total .................:16368,0BGZZ(1):ZZ(16384)128:ZZ13ZZ81ZZ1131310]G(16368,0:ZZ131500dGxPrGERR ANALG(16);10);"Total Error Analysis";:11::=H5:34:"Average";:6:36:"per":7:8:"Error";:24:"Number";:34:"Problem";:8:7:3(G$))G$:15SF"Total ........................... ";:G$(E1E2):3(G$))G$kFZZE1E2:ZZ2ZZ2F19:ME$(3ZZR(3)1)FE3E3E1:E4E4E2F PN%İ12000:1500 G22:6:"Press RETURN for next problem."::13:"Press Q to quit.";lem #";P;:7::P9ĺ(15);(15);"_";(15);(16);E5:8:"Error";:33:"Number";:8:(15);(15);"_____";:33:"______";(15);(16)F9:"Multiplying Terms ............... ";:G$(E1):3(G$))G$:11:"Combining Like Terms ............ ";:G$(E2):)16(42206)192Č47731'DT(43626):6DPROBLEMS D(16):3:N$","::"you may try up to 9 problems."::"How many would you like? ";DG$:N%(G$):N%01020:G$;DLE30:E40:P1N%:2000DERR SUM0E(16);6);"Error Summary for Prob1'CG1$;:ZZ4855000,40000,1000,3000C"2006C,AC6(16)C@9:T$"Thank you, "N$".":(40(T$))2)T$:" I hope you enjoyed this program.":" Press RETURN to reboot the disk.":20:16368,0DJP$:P$(13)330:(42204)238(4220518:(9);:"Menu":(14):8:5:"1) Instructions":B5:"2) Learn about the FOIL method"::5:"3) Work on problems"::5:"4) Exit the program"B18:8:"Your selection: ";BG1$:G1$"1"G1$"4"255:ZZ(G1$)C16368,0:ZZ50ZZ51MQ%1(4000):N$N$((4000ZZ)):ZZ:MQ%(4000ZZ):53000:200\A50000:51000:52000:53000A(16);:4:"Hi, ";N$;"!":::"This program will help you practice"::"multiplying binomials using the FOIL"::"method.":12000A MENU4B(16);:4:JP@ BINOMIAL MULTIPLICATION8@ COPYRIGHT (C) 1983 BYV@ MICROCOMPUTER WORKSHOPS k@PORTCHESTER, NY@LAST UPDATE: 11/28/84@ BY: KEVIN VESSIO@dR(X)(X(1)1)@nSIGN(X)32R(2)@xVAR(X)119R(3)""" ""  ">"6**"""""&*2""""""""""""*,"" "" ">"""""""""""""**6"""">>>> "(~ < (&20 *, >> """@8p``8@p""< >> "L <"<"""<< <"""<"><$""< """"  "" 6***""""""""""<""< :< $"""2,"""**6""">>8  80 >YEEY>">""""""""""""">>><2"<""">""" ""  ">"6**"""""&*2""""""""""""*,"" "" ">"""""""""""""**6"""">>>> >00000>"(~ < (&20 *, **>> "2*&" " >> ">> """>""""""< >> "&<]gjnA 'FNVry);@CQZ`cfiknAq%svz} !A%u)A-:=h ,5>BFIKMOQSUY[]_acegikmoqsuwy{} <"<"""<< <"""<"><$""< """"  "" 6***""""""""""<""< :< $"""2,"""""**6"""""< >>8  80,"*:<"">""""""""""""">>><2"<""">""" ""  ">"6**"""""&*2""""""""""""*,"" "" ">""""""""""""""**6"""""""> >>> >00000>">>< (&20 *, **>> "2*&" " >>  ">> "8""> """"""< >> "$$! $%%#,fp% "Lp"% $`"H Β*+)hi#"H Β!*0+i+idH#d hd`"%$$%H hi#`$% Βc,d*+Me,dPMc*!0 +i+`%J) b+je *`PPPP򠥹,r0tL"$!e (' !!%##`f`" e$$ ",r0st(!#L"L $b . % `L a,gPgA[8 & & &mh)mi ̒e$*+Me$(Mc,dp ,cpP!pA* +i+Mes@`p0  80`@p300p0030\xppฮ|@@`p8p`p|Օ@p`p8`p p pxฮB|p p `?``Օa@: @@8`7 7 S S S S 0p06 p@9 `88 0<710 @# Ff@@~~" 8p`@@@@@@`p0? @@@`p8@s0`@xy?``? 80p``@@@@@``00 x x x8` |  c``ag# #  ??# g``c```g7  LLOLLL  XpxC `0 @!~cffc```@x | Cx q33s3331!`?@xx윀@8yյCp@0800OꚆa`8~ 0`@``յC@@`0 ``Ꚇa F~~8`8`ccffc``agCffCaGqCf`fC`xN<8`@?`@@@ppqx@|뛇p``0 ?`?@յ|?``?px x xꚆaxx x @@յC?`xppꚆ` ! S S pp07 8`: @p9 8>30 @$ FfF@ #  0`@@@@`0? @@`0 a303a `08  0p`@q30p0031 Xp   56)256):1,(LOC256)!A$230,64AA((4);"BLOAD LOGO.PAC,A"LOCMA2UNPACK^A<4:0,110,1AF16304,0:16297,0:16302,0:16299,0APZ12500:Z:::10:16:"LOADING":12:8:"BINOMIAL MULTIPLICATION":(4);"RUN HELLO"E500:``U~UcU~4:5 $ L <"<"""<< <"""<"><$""<   "" 6***""""""""""<""< :< $"""2,"*"""<>>8  80 roduct of each pair of":FE "terms (First, Outside, Inside, Last)":WE"in order."bE 10000E " If you make a mistake, I will help":E "you by pointing to the terms you should":E "be multiplying."::UF " Remember";:ZZ18:(8)100007D" When you decide to work on problems,":gD"I will make one up and display it near":D"the top of the screen."::D" Then you will multiply the binomials":D"using the FOIL method. I will ask you":E"to enter the p Second";:ZZ16:(8);::(15);(15);"______";(15);(16);": I will explain how FOIL":jC$"works.":C." Third";:ZZ15:(8);::(15);(15);"_____";(15);(16);": We will do another problem":C8"which will be harder than the first."DB If you choose to let me teach you":UB"about the FOIL method, we will do three":fB"things:":B" First";:ZZ15:(8);::(15);(15);"_____";(15);(16);": I will show you how to use":B"FOIL by helping you do a problem.":ZC" the FOIL":AP"method."::LAZ" There are two ways I can help you.":{Ad"The first way is by teaching you some":An"things about the FOIL method, and the":Ax"second way is by giving you problems":A"to work on."A10000$B" 9@ ZZ1(4000):N$N$((4000ZZ)):ZZ:MQ%(4000ZZ)@(16);14);"Instructions";:I112:(8);:I:(15);(15);"____________";(15);(16)@@("Okay, ";N$;","@2@<" I will help you learn about": AF"multiplying binomials using     ЍŠŠŠĠԍ΍ (0 Zнй`)JJ & & f)` "  ??" g```c```g6 : ?`@`?p@6 6 S 2aՀ  p333s3330?`C@`?x@!`yp`p 00``@@@@@``p08 p ppp@ |  accca``cf"aՀ `p8꺎C  LLLOLLL \xp ս Հ x~~`p8~C @agfga```@@p | x8p@?`@@`??`@`?`88`8axxx켌@yYa8`8008O@ฮ꺎C @p~8p`@@@@ ꊂx ՟~||p@p@1ƚagfga``cfgfgccg`g@p|Like Terms .. ";E4;:ZE4P:35:17000:jH17:"Total ................. ";E3E4;:Z(E3E4)P:35:17000:H21:9:"You completed "P" problem";:P1ĺ".":1570H"s."H"24:10:"Press "(9)"RETURN"(14)" for Menu.";:12020I@E10:E20:E30:20r Analysis";:11::G5:34:"Average";:6:36:"per":7:8:"Error";:23:"Number";:34:"Problem";:8:7:(15);(15);"_____";:23:"______";:34:"_______";(15);(16);G11:"Multiplying Terms ..... ";E3;:ZE3P:35:17000:&H13:"Combining E3E1:E4E4E2$F PN%İ12000:1500zF22:6:"Press RETURN for next problem."::13:"Press Q to quit.";:16368,0FZZ(1):ZZ(16384)128:ZZ13ZZ81ZZ1131310F(16368,0:ZZ131500FxPFERR ANALG(16);10);"Total ErroNumber";:8:(15);(15);"_____";:33:"______";(15);(16)E9:"Multiplying Terms ............... "E1:11:"Combining Like Terms ............ "E2:15:"Total ........................... "E1E2EZZE1E2:ZZ2ZZ2E19:ME$(3ZZR(3)1) FE3::"you may try up to 9 problems."::"How many would you like? ";cDG$:N%(G$):N%01020:G$;DLE30:E40:P1N%:2000DERR SUMD(16);6);"Error Summary for Problem #";P;:7::P9ĺ(15);(15);"_";(15);(16);:E5:8:"Error";:33:"1&CG1$;:ZZ4855000,40000,1000,300/C"2005C,@C6(16)nC@10:(30(N$))2:"All right, ";N$;".":CJ3:"Thanks for letting me work with you.":CT2:"I hope you enjoyed it as much as I did."C^20:CPROBLEMS BD(16):3:N$","18:(9);:"Menu":(14):8:5:"1) Instructions":B5:"2) Learn about the FOIL method"::5:"3) Work on problems"::5:"4) Exit the program"B18:8:"Your selection: ";BG1$:G1$"1"G1$"4"255:ZZ(G1$)C16368,0:ZZ50ZZ51MQ%1(4000):N$N$((4000ZZ)):ZZ:MQ%(4000ZZ):53000:200[A50000:51000:52000:53000A(16);:4:"Hi, ";N$;"!":::"This program will help you practice"::"multiplying binomials using the FOIL"::"method.":12000A MENU3B(16);:4:PM@ BINOMIAL MULTIPLICATION8@ COPYRIGHT (C) 1983 BYV@ MICROCOMPUTER WORKSHOPS k@PORTCHESTER, NY@ LAST UPDATE: 9/26/84@ BY: KEVIN VESSIO@dR(X)(X(1)1)@nSIGN(X)32R(2)@xVAR(X)119R(3);A}(4000)0N$"":ZZ                        ? ";:G1$"".KG1$:G1$"Y"G1$"y"ĺ"Y";:20JKG1$"n"G1$"N"5086\K"N";:(16);Kp12:(31(N$))2:"Good luck, ";N$;"."Kz4000,(N$):ZZ1(N$):4000ZZ,((N$,ZZ,1)):ZZ:4000ZZ,MQ%K(4);"RUN BINMULT"L' WAIT FOR USER TO HITchoose to quit"::J"or to continue doing problems."::kJ" When you finish a set of problems or":J"quit, I will give you a total error"::"analysis."J10000:(16) K10:5:"Would you like to review the"::5:"instructions (Y or N)s, enter":HI"their sum; if not, then press ";(9);"RETURN";(14);"."SI10000I" Once you combine like terms, you will"I"be done with the problem, and I will":I"give you a summary of your errors."::J" At this time, you may ask you to find and add any":JH"like terms. (For example, if your":H"answer is x~+5x-3x-15, then ";(9);"5x";(14);" and ";(9);"-3x";(14):H"are like terms, and their sum is ";(9);"2x";(14);".)": I"If you find a pair of like term34)OG "as in ";(9);"y~";(14);". When you press ";(9);2;(14);", I will":oG "know which one you mean."zG 10000G" After you finish multiplying the":G"binomials, it will be time to simplify":G"the product."::H" I will;::(15);(15);"________";(15);(16);": The ";(9);2;(14);" key is a special key"F "for me. You may use it when you mean":F "the number two, as in ";(9);"2x";(14);"; or you may use"G "it when you mean the exponent ";(34);"squared,";(ain."X8;12000:16000:11000nX`;"Product of ";PN$;" terms: ";:V14:H18(PN$):13000:G$""İ16000:15200Xj;C1$G$:30000:C15500Xt;E1E11X;16:1:"Sorry, ";N$;".":X;PA%2CO%(1,2)0ĺ"-"; Y;PR$(1(PA%2));" * ";:(PA%2PA%4)CO%(4)"nside":15100-W:PN$(9)"L"(14)"ast"WW:14000:VA$PR$:CO%PR%:10500:C2$RE$W;"Product of "PN$" terms: ";:V14:H18(PN$):13000:G$""İ16000:15110W ;C1$G$:30000:C15500W;E1E11X.;16:1:"That's not right, ";N$;"."::"Try agR%CO%(1,2)CO%(2,2):VA$(1,2)VA$(2,2)PR$VA$(1,2)VA$(2,2):ZVJ8PR$VA$(2,2)VA$(1,2):jV:ENTER TERMuV:16000V:ZH(0):PA%15030,15040,15050,15060V:PN$(9)"F"(14)"irst":15100V:PN$(9)"O"(14)"utside":15100W:PN$(9)"I"(12,1)PR$VA$(1,1)VA$(2,1):7U7PR$VA$(2,1)VA$(1,1):|Ux7PR%CO%(1,1)CO%(2,2):VA$(1,1)VA$(2,2)PR$VA$(1,1)VA$(2,2):U7PR$VA$(2,2)VA$(1,1):U7PR%CO%(1,2)CO%(2,1):VA$(1,2)VA$(2,1)PR$VA$(1,2)VA$(2,1):U7PR$VA$(2,1)VA$(1,2):>V@8P"Z"ZZ$"a"ZZ$"z"G1$"~"JT,3ZZ:G$G$G1$:ZGZG1:H:V:G$;:13030WT6PRODUCTT6ZG(0):PA%14100,14200,14300,14400:(PR$,1)"a"(PR$,1)"z"(PR$,2)(PR$,1)(PR$,1)PR$(PR$,(PR$)1)"~"T6U7PR%CO%(1,1)CO%(2,1):VA$(1,1)VA$($G$G1$:ZGZG1:H:V:G$;:13030OS2G1$(13)ĭ(G$,1)"-"(G$,1)"+"13030`S2G1$(13)ıuS2G1$(8)13090S3G$""ĺG1$;" ";G1$;S3(G$)1ZGZG1:G$(G$,(G$)1):13030S3ZG0:G$"":13030T"3ZZ1(G$):ZZ$(G$,ZZ,1):ZZ$"A"ZZ$2G$"0"G$"-0"G$"+0"13030@R2(G1$"-"G1$"+")ZG013030R2ZG0ĭG1$"2"ĭ((G$,1))119ĭZH((G$,1))(ZH47ZH58)13030R2ZG0ĭ((G$,1))12613030R2G1$"x"G1$"y"G1$"z"ĭZG0āZZ1(G$):(G$,ZZ,1)G1$13030:!S2G1$"2"G12020"Q.16368,0:24:7:30);:3Q2Get routineWQ2ZG(0):G$"":G1$"":ZG0:V:HQ2G1$:(G1$)87(G1$)91G1$((G1$)32)Q2ZH(G1$):ZH1313050:ZH813060:ZH43ZH45ZH4813030Q2(ZH57ZH120)ZH12213030Q2ZG1113030R1100AP*+HS%7(HP%(PR$(1))(PR$(2))4(PR$(3)))3.5(PR$(4))VP\+48:1:3(ER%)pPf+1HF%,VB%:1HS%,VB%Pp+HF%,VB%HF%,VT%HS%,VT%HS%,VB%Pz+P.RETURNP.16368,0:24:9:"Press RETURN to continue.";Q.ZZ(1):ZZ(16384):ZZ141)CO%1RE$"-"VA$:*O)CO%0RE$"0":?O")RE$(CO%)VA$:KO* POINTgO+VB%8VP%10:VT%VB%10O +PA%3HF%7HP%3.5(PR$(1)):11040O+HF%7(HP%(PR$(1))1)3.5(PR$(2))P +PA%1PA%3HS%7(HP%(PR$(1))(PR$(2))3)3.5(PR$(3)):10500:PR$(3)RE$AN8'CO%(CO%(2,2)):VA$VA$(2,2):10500:PR$(4)RE$uNB'VP%:HP%:"(";PR$(1);:CO%(1,2)0ĺ"-";:10070NL'"+";NV'PR$(2);")(";PR$(3);:CO%(2,2)0ĺ"-";:10090N`'"+";Nj'PR$(4);")":N)VA$""RE$(CO%):N)CO%1RE$VA$:O)(CO%0):H3%H3%2M\20000aMf16000:"Nice job, ";N$;"."::"You're done with this problem."nMp12000:{M'DISPLAYM'CO%CO%(1,1):VA$VA$(1,1):10500:PR$(1)RE$M$'CO%(CO%(1,2)):VA$VA$(1,2):10500:PR$(2)RE$N.'CO%CO%(2,1):VA$VA$(2,1):1H3%(RE$)(CO%0):H3%H3%2:2140LHH3%41:PA%1:14000:VA$PR$:CO%CO%(1,1)CO%(2,1)CO%(1,2)CO%(2,2):10500:H3%H3%(RE$)(CO%0)((RE$)CO%0):PA%2:14000:VA$PR$:CO%PR%:10500:H3%H3%(RE$)MRPA%3:14000:VA$PR$:CO%PR%:10500:H3%H3%(RE$1)VA$(1,1)VA$(2,2)2120*K*H3%H2%:2140K4H3%41:PA%2:14000:VA$PR$:CO%CO%(1,2)CO%(2,1)CO%(1,1)CO%(2,2):10500:H3%H3%(RE$)(CO%0)((RE$)CO%0):PA%1:14000:VA$PR$:CO%PR%:10500:H3%H3%(RE$)!L>PA%4:14000:VA$PR$:CO%PR%:10500:H3%009J12:1:"________________________________________";J V2%8:H2%41:I14:PA%I:14000:CO%PR%:VA$PR$:10500:H2%H2%(RE$)(I1CO%0):I:H2%H2%2:I14:PA%I:15000:IJV3%11:VA$(1,1)VA$(2,1)VA$(1,2)VA$(2,2)2100K VA$(1,2)VA$(2,0 IPROBLEM"IE10:E20:25000I(16);14);"Problem #";P;:15:(15);(15);"__________";(15);(16);:P9ĺ(15);(15);"_";(15);(16);JVP%5:HP%37:I12:J12:CO%CO%(I,J):VA$VA$(I,J):10500:HP%HP%(RE$)(J2CO%0):J,I:HP%HP%2:1001,2)SIGN(0)R(7):VA$(1,2)"":CO%(2,1)SIGN(0)R(7):VA$(2,1)(VAR(0)):CO%(2,2)SIGN(0)R(7):VA$(2,2)""hBcVA$(1,1)VA$(2,1)25400hLc(2)1VA$(1,2)VA$(2,1):hVcVA$(2,2)VA$(1,1): icR(10)25510,25600,25700,25800,25510,25600,25700,258005400gbCO%(1,1)SIGN(0)R(7):VA$(1,1)(VAR(0)):CO%(1,2)SIGN(0)R(7):VA$(1,2)"":CO%(2,1)SIGN(0)R(7):VA$(2,1)(VAR(0)):CO%(2,2)SIGN(0)R(7):VA$(2,2)""gbVA$(1,1)VA$(2,1)25310gbnh8cCO%(1,1)SIGN(0)R(7):VA$(1,1)(VAR(0)):CO%((1,1)SIGN(0)R(7):VA$(1,1)(VAR(0)):CO%(1,2)SIGN(0)R(7):VA$(1,2)(VAR(0)):CO%(2,1)SIGN(0)R(7):VA$(2,1)VA$(1,1):CO%(2,2)SIGN(0)R(7):VA$(2,2)VA$(1,2)fzbCO%(1,1)CO%(2,2)CO%(1,2)CO%(2,1)0VA$(1,1)VA$(1,2)25200fbgbR(2)22,25500e bR(8)525200ebCO%(1,1)SIGN(0)R(7):VA$(1,1)(VAR(0)):CO%(1,2)SIGN(0)R(7):VA$(1,2)"":CO%(2,1)SIGN(0)R(7):VA$(2,1)VA$(1,1):CO%(2,2)SIGN(0)R(7):VA$(2,2)VA$(1,2)e bCO%(1,1)CO%(2,2)CO%(1,2)CO%(2,1)025110e*bfpbCO%"+"dOTM$TM$C1$UdOPA%3:14000:CO%PR%:VA$PR$:10500:(RE$,1)"-"TM$TM$"+"zdOTM$TM$RE$:((41(TM$))2)TM$;dOV2%1:1:80);:dPG$""LT%C1:dPG$""LT%G$""LT%C0:d(PC2$G$:30000:daCREATE PROBeaR(10)25300ceO(C1$,1)"-"TM$TM$"+".cjOTM$TM$C1$qcoOPA%4:14000:CO%PR%:VA$PR$:10500:(RE$,1)"-"TM$TM$"+"ctOTM$TM$RE$:((41(TM$))2):TM$;:20400c~OPA%2:14000:CO%PR%:VA$PR$:10500:TM$RE$:(C1$,1)"0"20380dO(C1$,1)"-"TM$TM$Ⱥ:PA%1:14000:T1%PR%:CO%PR%:VA$PR$:10500:RE$;" + ";:PA%4:14000:T1%T1%PR%:CO%PR%:10500:RE$;" = ";:CO%T1%:10500:RE$:12000:20200bLOLT%20400bVO11:TM$"":LT%120350b`OPA%1:14000:CO%PR%:VA$PR$:10500:TM$RE$:(C1$,1)"0"20335he product are"::"like terms.":12000:20200aOLT%1Ģ20:1:"Sorry, ";N$;"."::PA%2:14000:T1%PR%:CO%PR%:VA$PR$:10500:RE$;" + ";:PA%3:14000:T1%T1%PR%:CO%PR%:10500:RE$;" = ";:CO%T1%:10500:RE$:12000:20200bO20:1:"Sorry, ";N$;".":B%HS%,VB%HS%,VT%`N12000`N16000:16:"Press RETURN if there are no like terms.":14:"Enter sum of like terms: ";:V14:H27:13000:20500:C20300`NE2E21-aNLT%Ģ18:1:"You can't combine any terms, ";N$;".":20:"None of the terms in t%3:14000:VA$PR$:CO%(PR%):10500:HS%T1%3.5(RE$)_NLT%1T1%T1%7(RE$)7:PA%4:14000:VA$PR$:CO%(PR%):10500:HS%T1%3.5(RE$):PA%1:14000:VA$PR$:CO%PR%:10500:HF%7(H2%1)3.5(RE$)`N1:16:3:1HF%,VT%:1HS%,VT%:HF%,VT%HF%,V":12000:20200Y^N20:1:"Not quite, ";N$;". You have made"::"an error in addition."t^NVT%8V2%3:VB%VT%106_NPA%1:14000:VA$PR$:CO%PR%:10500:T1%7(H2%(RE$)):PA%2:14000:VA$PR$:CO%(PR%):10500:HF%T1%3.5(RE$):T1%T1%7(RE$)7:PA":14:"Enter sum of like terms: ";:V14:H27:13000:20500:C20300P]NE2E21]NLT%G$""Ģ20:1:"Sorry, ";N$;", there is a pair"::"of like terms.":20150^NLT%Ģ20:1:"That is incorrect, ";N$;". There"::"are no like terms in the product.CO%CO%(1,1)CO%(2,2)CO%(1,2)CO%(2,1):10500:C1$RE$:20090\\NVA$(1,2)VA$(2,1)VA$(1,1)VA$(2,2)LT%1:PA%1:14000:VA$PR$:CO%CO%(1,1)CO%(2,1)CO%(1,2)CO%(2,2):10500:C1$RE$\zN12000D]N16000:16:"Press RETURN if there are no like terms.[B[ NCOMB LIKE TERMSq[*N16000:"Good work, ";N$;". You have"::"finished the multiplication. Now you":[4N"must simplify the product by combining"::"any like terms."<\RNLT%0:VA$(1,1)VA$(2,1)VA$(1,2)VA$(2,2)LT%1:PA%2:14000:VA$PR$:ZZ1PR%0)(RE$):ZZ:PA%T2%.ZCLEAR MESSAGEgZ>13:1:(22);(16);(25);:14:1mZ>ZhB DISPLAY #/2DEC PLACESZmBZ(Z100.5)100ZrBZZ(Z):ZZ;".";Z|BZZZZZ:(ZZ10.0001);ZBZZZZ((ZZ10.0001)10):(ZZ100.1);2,2)0ĺ"-";2Y;PR$(3(PA%2(PA%2)));" = ";C2$KY;12000:16000:15200iY3:1:" Now that you know how to multiply"::"binomials with FOIL,4:ER%0:11000:15000vl16000:" By adding -14y to the sum, we have"::"finished all four letters of FOIL. Now"::"we try to simplify the product.":12000Cwv16000:" Since the product has no pairs of"::"like terms, it can't be simplified. try finishing the problem."::"We're up to the third letter in FOIL.":12000:PA%3:ER%0:11000:15000vD16000:"Good work, ";N$;"."::" Notice that I've added -2xy to the"::"other two terms. All we have left are"::"the last terms.":12000:PA% The second letter in FOIL is O. The"::"product of the outside terms (3x and 7)"::"is 21x.":12000t16000:" Continue to build the answer by"::"adding 21x to 3x~."t7:1:120);:8:13:"3x~+21x":12000:ER%1:11000gu:16000:" Now you I"::"put 3x~ on the next line as the first"::"term in the solution."sV2%8:H2%13:PA%1:14000:VA$PR$:CO%PR%:10500:V2%:H2%:RE$:C1$"2 1234 5 6781":V2%1:H2%1:C1$s12000:ER%1:11000:ER%0:PA%2:11000s16000ft" l right, ";N$;", let's try an"::"example. I'll start it off.":12000:16000r֜" The first letter in FOIL is F, so I"::"begin by multiplying the first term of"::"each binomial.":PA%1:11000:12000Is16000:" The product of 3x and x is 3x~. just add them to get the answer."/qr16368,0Gq|12000:2:1:(6);qVP%5:HP%15:CO%(1,1)3:VA$(1,1)"x":CO%(1,2)2:VA$(1,2)"y":CO%(2,1)1:VA$(2,1)"x":CO%(2,2)7:VA$(2,2)"":10000q12:1:"________________________________________"Mr"Al16:"F irst":16:"O utside":"is short for: I nside":16:"L ast"!qh12:" FOIL helps you remember to take the"::"products of the first, outside, inside,"::"and last terms of the two binomials."::"Once you have found the four products,"::"youZ1$ oyZZoyZ$ZZ$:&o@TutorialoJ(16);4);"The FOIL method: How to use it":1:4);(15);(15);"_______________________________";(15);(16)oT3:1:" The FOIL method is a technique for"::"multiplying binomials. The word FOIL":Bp^yZ$ZZ$n^yZ$"-1"31170$n|yZZ$""`nyZZ1(Z$):Z1$(Z$,ZZ,1):Z1$"1"ZZ$ZZ$Z1$:31160pnyZZ131150ny(Z$,ZZ1,1)"0"(Z$,ZZ1,1)"9"(Z$,ZZ1,1)"0"(Z$,ZZ1,1)"9"ZZ$ZZ$Z1$ny31160oy(Z$,2,1)"0"(Z$,2,1)"9"ZZ$ZZ$C1$)0(C2$)0TmluC(C1$)2ZZ$(C1$,(C1$)2)(C1$,1)((C1$,2),1):CZZ$C2$ZmvulmyPREP STRINGSm,yZZ$"":ZZ1(Z$):Z1$(Z$,ZZ,1):Z1$" "Z1$"("Z1$")"Z1$"+"31050m6y(Z1$)64(Z1$)91Z1$((Z1$)32)m@yZZ$ZZ$Z1$mJyZZnT8ldR(2)2CO%(1,1)CO%(1,1)ZZ:CO%(1,2)CO%(1,2)ZZ:hldCO%(2,1)CO%(2,1)ZZ:CO%(2,2)CO%(2,2)ZZ:vl0uCOMP $'Sl:uC1$C2$C1:lDuC1$""C2$""C0:lNuZ$C1$:31000:C1$Z$lXuZ$C2$:31000:C2$Z$mbuCC1$C2$(C1$,1)"0"(C2$,1)"0"()ZZ)25600kdZZk(dWkdd25510:ZZR(2)1:(ZZCO%(1,1))7(ZZCO%(1,2))725700kndR(2)2CO%(1,1)CO%(1,1)ZZ:CO%(1,2)CO%(1,2)ZZ:kxdCO%(2,1)CO%(2,1)ZZ:CO%(2,2)CO%(2,2)ZZ:kd25600:ZZR(2)1:(ZZCO%(1,1))7(ZZCO%(1,2))725800jdCO%(1,1)SIGN(0)R(7):VA$(1,1)(VAR(0)):CO%(1,2)SIGN(0)R(7):VA$(1,2)(VAR(0)):CO%(2,1)CO%(1,1):VA$(2,1)VA$(1,1):CO%(2,2)CO%(1,2):VA$(2,2)VA$(1,2)j dVA$(1,1)VA$(1,2)25600 kdZZ25:CO%(1,1)ZZ(CO%(1,1)ZZ)CO%(1,2)ZZ(CO%(1,2,25510,25600icCO%(1,1)SIGN(0)R(7):VA$(1,1)(VAR(0)):CO%(1,2)SIGN(0)R(7):VA$(1,2)"":CO%(2,1)CO%(1,1):VA$(2,1)VA$(1,1):CO%(2,2)CO%(1,2):VA$(2,2)VA$(1,2)icZZ25:CO%(1,1)ZZ(CO%(1,1)ZZ)CO%(1,2)ZZ(CO%(1,2)ZZ)25510icZZic15:9:"Microcomputer Workshops":17:15:"Courseware":19:17:"@ 1984"ú(9);:ZZ140:1:ZZ:" ";:23:ZZ:" ";::ZZ122:ZZ:1:" ";:40:" ";::(14);ÁZZ12500:ZZ:ӈ8DzLOAD/INIT SHAPE TABLE`Ǻ(13);(4);"BLOAD SHAPES":232,0:233,"may not cancel each other completely.":12000h(16):12:12:"Enjoy the problems!":ZZ13000:ZZ:sPòTITLEZÑ:16302,0:(1);1ڇdâ7:9:"Binomial Multiplication":10:5:"By Mark Berman and Kevin Vessio"Hxâ12:11:"Designed by Don Ross":"middle terms will cancel. In some"::"other cases (like the first practice"::"problem), you will not be able to"::"combine like terms at all.":12000-16000:" But in most cases, you will be able"::"to combine like terms, although they"::2000:40920k11:19:"x~-49":16000:"Excellent, ";N$;"."::" Notice that in this problem, the sum":Dž"of the like terms is zero, so the middle":"two terms dropped out completely.":12000 16000:" In a few cases (like this one), the"::%:1HS%,VT%:HF%,VT%HF%,VB%HS%,VB%HS%,VT%:12000:V2%1:1:80)؟H30:16000:"Enter sum of the like terms: ";:13000:Z$G$:Z$""40920ݟ31000:Z$"0"Z$"-0"Z$"+0"40950 ⟖1:18:"That's not the correct sum, ";N$;"."::"-7x + 7x = 0":1000:Iğ16000:" Here's the twist. In this product,"::"the second and third terms are like"::"terms. To get the final answer, you"::"must simplify by combining like terms."CΟVT%8V2%3:VB%VT%10:HF%7H2%17.5:HS%HF%21:3:16:1HF%,VT"x":CO%(2,2)7:VA$(2,2)"":10000:V2%8:H2%16:V2%:H2%:"x~"ꂈ16000:" I've started you off on this problem"::"by filling in the product of the first"::"terms. Now you try doing the rest of"::"the FOIL sequence.":12000I24:PA%I:15"to do most of the work, but I'll help"::"at the end. (This problem has a little"::"twist to it.)":12000:2:1:(6):12:"________________________________________">~VP%5:HP%16:CO%(1,1)1:VA$(1,1)"x":CO%(1,2)7:VA$(1,2)"":CO%(2,1)1:VA$(2,1)istributive and commutative laws.":12000`(16);4);"The FOIL method: Extra practice":1:5:(15);(15);"________________________________";(15);(16):j" Before you start working on problems,":"let's try one more example. You'll have"tthe distributive":6L"and commutative laws.":12000Q16000:" Since we can distribute and commute"::"with any binomials, we know that FOIL":V"can be used whenever we multiply two"::"binomials. FOIL is just a shortcut for":(["the dZZ:"+ 21x ":10:14ZZ:" - 2xy":QQ1150:QQ,ZZq~.8:15:5);:9:15:"+ 21x":10:21:5);:9:21:"- 2xy"~811:13:"Outside Inside":112,80119,73:182,80168,73B16000:" Now you can see that FOIL gives the"::"same result as using turn FIOL into FOIL."}11:4:"First Inside Outside Last":3:40,8077,73:112,80119,73:182,80168,73:231,80210,73}12000}10:13:17);:11:13:19);:9:15:11);2~10:15:"- 2xy":8:21:"+ 21x":QQ1150:QQ:ZZ16:8:21"the result. Does it seem familiar?":12000|ޞ16000:" It should look very familiar. It's"::"the same result we found with FOIL,":|螺"except that the second and third terms"::"have been exchanged. We can use the":}"commutative law to "manageable pieces. The only thing left"::"to do is the multiplication.":12000w{9:11:"3x~ - 2xy + 21x - 14y"{ʞ16000:" That's it, ";N$;". We have"::"multiplied two binomials, using the":+|Ԟ"distributive law. Look carefully at":: (x+7).":12000lz16000:" Now, we use the distributive law"::"again on each of the two parts.":12000z7:5:"[(3x*x)+(-2y*x)]+[(3x*7)+(-2y*7)]"z16000:" By using the distributive law, we"::"have broken the original problem into":S{_______________________________"wy\14:" The first step is to use the"::"distributive law to split the product":yf"into two parts.":12000yp5:8:"(3x-2y)(x) + (3x-2y)(7)"zz16000:" Notice that I have distributed"::"(3x-2y) overֹ4000ZZ,MQ%1ֺ(16):12:15:"Please wait."N׺(4);"RUN INSTRUCTIONS"OZdֹ4000ZZ,MQ%ֺ(16):12:15:"Please wait."׺(4);"RUN INSTRUCTIONS"IPlease wait."ҍ׺(4);"RUN INSTRUCTIONS"Chain to instructions.#ֹ4000,(N$):Zlmost made it on that one."GNME$(6)"These problems are not so easy."yXME$(7)"Keep trying, "N$". You'll get it."bME$(8)"Don't be discouraged. You'll get better.":ƌֲ CHAIN TO INSTRֹ4000,(N$):ZZ1(N$):4000ZZ,((N$,ZZ,1)):ZZESSAGES,ME$(0)"Very impressive, "N$"!"`ME$(1)"I see you've been doing your homework."&ME$(2)"Too bad your teacher can't see this."0ME$(3)"Well, we can't all be perfect.":ME$(4)"Okay "N$", that was a good try."DME$(5)"You a<˭ZH65ZH12252025,=˭ZH90ZH9752025F>˭ZZ0ĭZH90ZHZH32`@˭ZZ0ĭZH97ZHZH32C˺(ZH);:ZZZZ1:N$N$(ZH):52025H˭ZZ052025ΊM˺(8)" "(8);:ZZ1G$"":G1$"":N$"":ZZ0:52025NN$(N$,(N$)1):ZZZZ1:52025ϲ INIT M3: ˲NAME*˺(16);:::" Please enter your first name (up to"::" ten letters) and press .":::10)"Name: ";4ZZ0:N$"":G1$"":ZH0ۉ9˾G1$:XX((78)(79))16:XX(XX):ZH(G1$):ZH13ZZ0ı:˭ZH852040;˭ZZ10520252).N'Pass variable names2N'in VA$(1-2,1-2). bN'CO%CO%(1,1):VA$VA$(1,1):10500:PR$(1)RE$N$'CO%(CO%(1,2)):VA$VA$(1,2):10500:PR$(2)RE$N.'CO%CO%(2,1):VA$VA$(2,1):10500:PR$(3)RE$N8'CO%(CO%(2,2)):VA$VA$(2,2):10500:PR$(4)RE$,OB'V(RE$)NMRPA%3:14000:VA$PR$:CO%PR%:10500:H3%H3%(RE$)(CO%0):H3%H3%2YM\20000Mf16000:"Nice job, ";N$;"."::"You're done with this problem."Mp12000:M'Display routineM'Print a problem.M'Pass coefficientsN'in CO%(1-2,1-:H3%H3%(RE$)]L>PA%4:14000:VA$PR$:CO%PR%:10500:H3%H3%(RE$)(CO%0):H3%H3%2:2140MHH3%41:PA%1:14000:VA$PR$:CO%CO%(1,1)CO%(2,1)CO%(1,2)CO%(2,2):10500:H3%H3%(RE$)(CO%0)((RE$)CO%0):PA%2:14000:VA$PR$:CO%PR%:10500:H3%H3%A$(1,1)VA$(2,1)VA$(1,2)VA$(2,2)2100TK VA$(1,2)VA$(2,1)VA$(1,1)VA$(2,2)2120fK*H3%H2%:2140L4H3%41:PA%2:14000:VA$PR$:CO%CO%(1,2)CO%(2,1)CO%(1,1)CO%(2,2):10500:H3%H3%(RE$)(CO%0)((RE$)CO%0):PA%1:14000:VA$PR$:CO%PR%:10500(I,J):10500:HP%HP%(RE$)(J2CO%0):J,I:HP%HP%2:10000uJ12:1:"________________________________________";J V2%8:H2%41:I14:PA%I:14000:CO%PR%:VA$PR$:10500:H2%H2%(RE$)(I1CO%0):I:H2%H2%2:I14:PA%I:15000:I&KV3%11:V;E3E4;:Z(E3E4)P:35:17000:*I"120000I@EIDo one problem.SIE10:E20^I25000I(16);14);"Problem #";P;:15:(15);(15);"__________";(15);(16);:P9ĺ(15);(15);"_";(15);(16);=JVP%5:HP%37:I12:J12:CO%CO%(I,J):VA$VA$23:"Number";:34:"Problem";:8:7:(15);(15);"_____";:23:"______";:34:"_______";(15);(16);H11:"Multiplying Terms ..... ";E3;:ZE3P:35:17000:H13:"Combining Like Terms .. ";E4;:ZE4P:35:17000:I17:"Total ................. "ext problem, Q to quit.";:16368,0]GZZ(1):ZZ(16384)128:ZZ13ZZ81ZZ1131310xG(16368,0:ZZ131500GxPGFinal Error Summary.G(16);10);"Total Error Summary";:11::cH5:34:"Average";:6:36:"per":7:8:"Error";:erms ............... ";E1IF11:"Combining Like Terms ............ ";E2}F15:"Total ........................... ";E1E2FZZE1E2:ZZ2ZZ2F20:ME$(3ZZR(3)1)FE3E3E1:E4E4E2F PN%İ12000:1500$G24:1:"Press RETURN for nP1N% EV2000:Do the problem.:EPrint error summary.E(16);6);"Error Summary for Problem #";P;:7::P9ĺ(15);(15);"_";(15);(16);E5:8:"Error";:33:"Number";:8:(15);(15);"_____";:33:"______";(15);(16)F9:"Multiplying TD^20:+DRun through a set of problems.D(16):3:N$","::"you may try up to 20 problems."::"How many would you like? ";:V7:H26:13000:NU$G$D(NU$)31010D(NU$)((NU$))(NU$)1(NU$)201010DN%(NU$)DE30:E40EL8:ZZ49ZZ522602C16368,0:ZZ50ZZ51MQ%1RCZZ4855000,40000,1000,300[C"200aC,lC6(16)C@10:(30(N$))2:"All right, ";N$;".":CJ3:"Thanks for letting me work with you.":CT2:"I hope you enjoyed it as much as I did.""method."::OB"What would you like to do?"::"1) Read the instructions":xB"2) Learn about the FOIL method":B"3) Work on problems":B"4) Exit the program"B23:"Enter one of the above."B16368,0CZZ(1):ZZ(16384)12:MQ%(4000ZZ):150BA50000:51000:Title page, initialization.cA52000: GET STUDENT'S NAME.A53000:Set up end of problem messages. B(16);"Hi, ";N$;"!"::"This program will help you practice"::"multiplying binomials using the FOIL"::O@ BINOMIAL MULTIPLICATION.@ VERSION 1.0I@ COPYRIGHT (C) 1983 BYg@ MICROCOMPUTER WORKSHOPS |@PORTCHESTER, NY@dR(X)(X(1)1)@nSIGN(X)32R(2)@xVAR(X)119R(3)A}(4000)0N$"":ZZ1(4000):N$N$((4000ZZ)):ZZ                              !"1,1)CO%(2,2)CO%(1,2)CO%(2,1):10500:C1$RE$:20090^\NVA$(1,2)VA$(2,1)VA$(1,1)VA$(2,2)LT%1:PA%1:14000:VA$PR$:CO%CO%(1,1)CO%(2,1)CO%(1,2)CO%(2,2):10500:C1$RE$^zN12000<_N16000:16:"Press RETURN if there are no like terms.":14:"OMBINE LIKE TERMS.i]*N16000:"Good work, ";N$;". You have"::"finished the multiplication. Now you":]4N"must simplify the product by combining"::"any like terms."4^RNLT%0:VA$(1,1)VA$(2,1)VA$(1,2)VA$(2,2)LT%1:PA%2:14000:VA$PR$:CO%CO%(C2$;:\>Clear message area.D\>13:1:(22);(16);(25);:14:1J\>|\hBDisplay a real number to two decimal places.\mBZ(Z100.5)100\rBZZ(Z):ZZ;".";\|BZZZZZ:(ZZ10.0001);\BZZZZ((ZZ10.0001)10):(ZZ100.1);\B] N C;" = ";C2$"[;12000:16000:15200@[3:1:" Now that you know how to multiply"::"binomials with FOIL, you should also":;{H"understand ";(1);"2why";(1);"1 the FOIL method works."::"Let's take another look at the problem"::"we just finished roduct.":12000yv16000:" Since the product has no pairs of"::"like terms, it can't be simplified. The":"product of (3x-2y) and (x+7) is"::"3x~+21x-2xy-14y.":12000 z4(16);5);"The FOIL method: Why it works":1:5);(15);(15);"__________ice that I've added -2xy to the"::"other two terms. All we have left are"::"the last terms.":12000:PA%4:ER%0:11000:15000yl16000:" By adding -14y to the sum, we have"::"finished all four letters of FOIL. Now"::"we try to simplify the p by"::"adding 21x to 3x~."Sw7:1:120);:8:13:"3x~+21x":12000:ER%1:11000w:16000:" Now you try finishing the problem."::"We're up to the third letter in FOIL.":12000:PA%3:ER%0:11000:15000xD16000:"Good work, ";N$;"."::" Not2 1234 5 6781":V2%1:H2%1:C1$Wv12000:ER%1:11000:ER%0:PA%2:11000bv16000v" The second letter in FOIL is O. The"::"product of the outside terms (3x and 7)"::"is 21x.":12000w16000:" Continue to build the answerg the first term of"::"each binomial.":PA%1:11000:12000u16000:" The product of 3x and x is 3x~. I"::"put 3x~ on the next line as the first"::"term in the solution.",vV2%8:H2%13:PA%1:14000:VA$PR$:CO%PR%:10500:V2%:H2%:RE$:C1$"1:VA$(2,1)"x":CO%(2,2)7:VA$(2,2)"":10000bt12:1:"________________________________________"t"All right, ";N$;", let's try an"::"example. I'll start it off.":12000:16000;u֜" The first letter in FOIL is F, so I"::"begin by multiplyinside, inside,"::"and last terms of the two binomials."::"Once you have found the four products,"::"you just add them to get the answer."sr16368,0s|12000:2:1:(6);+tVP%5:HP%15:CO%(1,1)3:VA$(1,1)"x":CO%(1,2)2:VA$(1,2)"y":CO%(2,1);(16)erT3:1:" The FOIL method is a technique for"::"multiplying binomials. The word FOIL":r^16:"F irst":16:"O utside":"is short for: I nside":16:"L ast"sh12:" FOIL helps you remember to take the"::"products of the first, out)"9"(Z$,ZZ1,1)"0"(Z$,ZZ1,1)"9"ZZ$ZZ$Z1$@qy31160oqy(Z$,2,1)"0"(Z$,2,1)"9"ZZ$ZZ$Z1$wqyZZqyZ$ZZ$:q@TutorialrJ(16);4);"The FOIL method: How to use it":1:4);(15);(15);"_______________________________";(15)Z1$" "Z1$"("Z1$")"Z1$"+"31050Op6y(Z1$)64(Z1$)91Z1$((Z1$)32)_p@yZZ$ZZ$Z1$gpJyZZrpTyZ$ZZ$p^yZ$"-1"31170p|yZZ$""pyZZ1(Z$):Z1$(Z$,ZZ,1):Z1$"1"ZZ$ZZ$Z1$:31160pyZZ1311505qy(Z$,ZZ1,1)"0"(Z$,ZZ1,1)2ZZ$(C1$,(C1$)2)(C1$,1)((C1$,2),1):CZZ$C2$=ovuVoyPrepare strings fornoycomparison. Stripoyall spaces, () andoy+ from Z$. Make anyoycapital letters small.oyRemove excess 1's.o"yZZ$""%p,yZZ1(Z$):Z1$(Z$,ZZ,1):(N$,(N$)1):ZZZZ1:520256ϲInitialize messages.XME$(0)"Very impressive, "N$ME$(1)"I see you've been doing your homework."&ME$(2)"Too bad your teacher can't see this."0ME$(3)"Well, we can't all be perfect.":ME$(4)"Okay "NH13ZZ0ı:˭ZH852040-;˭ZZ1052025E<˭ZH65ZH12252025\=˭ZH90ZH9752025v>˭ZZ0ĭZH90ZHZH32@˭ZZ0ĭZH97ZHZH32C˺(ZH);:ZZZZ1:N$N$(ZH):52025njH˭ZZ052025M˺(8)" "(8);:ZZ1G$"":G1$"":ZZ0:52025NN$d init shape table.?`Ǻ(13);(4);"BLOAD SHAPES":232,0:233,3EDZ` ˲ GET STUDENT'S NAME.΋*˺(16);" Please enter your first name (up to"::" ten letters) and press .":::10)"Name: ";4ZZ0:N$"":G1$"":ZH0 9˾G1$:ZH(G1$):Z(1);1*dâ9:9:"Binomial Multiplication"Fnú:14:"By Mark Berman"jxú:9:"Microcomputer Workshops"~ú:17:"@ 1983"يú(9);:ZZ140:1:ZZ:" ";:23:ZZ:" ";::ZZ122:ZZ:1:" ";:40:" ";::(14);슌ÁZZ12500:ZZñ8DzLoad an.":1200016000:" But in most cases, you will be able"::"to combine like terms, although they"::"may not cancel each other completely.":12000ԉ(16):12:12:"Enjoy the problems!":ZZ13000:ZZ:PòPrint a title page.ZÑ:16302,0: middle":"two terms dropped out completely.":12000 16000:" In a few cases (like this one), the"::"middle terms will cancel. In some"::"other cases (like the first practice"::"problem), you will not be able to"::"combine like terms at all31000:Z$"0"Z$"-0"Z$"+0"40950v⟖1:18:"That's not the correct sum, ";N$;"."::"-7x + 7x = 0":12000:40920ׇ11:19:"x~-49":16000:"Excellent, ";N$;"."::" Notice that in this problem, the sum":3"of the like terms is zero, so theust simplify by combining like terms."ΟVT%8V2%3:VB%VT%10:HF%7H2%17.5:HS%HF%21:3:16:1HF%,VT%:1HS%,VT%:HF%,VT%HF%,VB%HS%,VB%HS%,VT%:12000:V2%1:1:80)؟H30:16000:"Enter sum of the like terms: ";:13000:Z$G$:Z$""40920$of the first"::"terms. Now you try doing the rest of"::"the FOIL sequence.":12000qI24:PA%I:15000:I%ğ16000:" Here's the twist. In this product,"::"the second and third terms are like"::"terms. To get the final answer, you"::"m______________________"~VP%5:HP%16:CO%(1,1)1:VA$(1,1)"x":CO%(1,2)7:VA$(1,2)"":CO%(2,1)1:VA$(2,1)"x":CO%(2,2)7:VA$(2,2)"":10000:V2%8:H2%16:V2%:H2%:"x~"V16000:" I've started you off on this problem"::"by filling in the product 15);(16):fj" Before you start working on problems,":"let's try one more example. You'll have"t"to do most of the work, but I'll help"::"at the end. (This problem has a little"::"twist to it.)":12000:2:1:(6):12:"__________________IL":_V"can be used whenever we multiply two"::"binomials. FOIL is just a shortcut for":["the distributive and commutative laws.":12000 `(16);4);"The FOIL method: Extra practice":1:5:(15);(15);"________________________________";(112,80119,73:182,80168,73~B16000:" Now you can see that FOIL gives the"::"same result as using the distributive":L"and commutative laws.":12000Q16000:" Since we can distribute and commute"::"with any binomials, we know that FO10:13:17);:11:13:19);:9:15:11);10:15:"- 2xy":8:21:"+ 21x":QQ1150:QQ:ZZ16:8:21ZZ:"+ 21x ":10:14ZZ:" - 2xy":QQ1150:QQ,ZZ݀.8:15:5);:9:15:"+ 21x":10:21:5);:9:21:"- 2xy"811:13:"Outside Inside":xcept that the second and third terms"::"have been exchanged. We can use the":"commutative law to turn FIOL into FOIL."11:4:"First Inside Outside Last":3:40,8077,73:112,80119,73:182,80168,73:231,80210,7312000)$", that was a good try."FDME$(5)"You almost made it on that one."sNME$(6)"These problems are not so easy."XME$(7)"Keep trying, "N$". You'll get it."ێbME$(8)"Don't be discouraged. You'll get better."lϱֲChain to instructions.4ֹ4000,(N$):ZZ1(N$):4000ZZ,((N$,ZZ,1)):ZZEֹ4000ZZ,MQ%hֺ(16):12:15:"Please wait."׺(4);"RUN INSTRUCTIONS"Z