1

MFM1P–Unit2:Algebra–Lesson1 Date:______________Learninggoal:Iunderstandpolynomialterminologyandcancreatealgebraicexpressions.

2.1IntrotoAlgebra

Whatisalgebra?

• Learningalgebraislikelearninganotherlanguage.Bylearningalgebra,mathematicalmodelsofreal-worldsituationscanbecreatedandsolved!

• Inalgebra,lettersareoftenusedtorepresentnumbers.

KEYTERMS

àvariable àcoefficient à expression

àconstantBrainstormwordsthatrepresent…

Addition Subtraction Multiplication Division

2

Chooseavariabletorepresentthenumberandwriteanalgebraicexpressionforthefollowingphrases.

a)19decreasedbyanumber b)30morethananumber

c)12morethan3timesanumber d)Anumberdividedbyseven

e)doubletheamountofmoney f)5yearsyoungerthanRebeccaWriteanEnglishstatementthatcouldrepresenteachofthefollowing:

a) g+5

b) 4d

c) 2a–1

3

Homework2.1VariablesandExpressions

1. Indicatewithmathsymbolswhatoperationsarebeingdescribedbythegivenword(s).Use

, -, x, or symbols.+ ÷ a)sum_____ b)product_______ c)decreasedby______ d)times_______ e)increasedby_____ f)difference_________ g)morethan______ h)lessthan_______ i)twicesomething______2. Writeaverbalexpressionforthealgebraicexpression. a)x+7 b)2x c)x–6 d)y2 e)3x–4 f)ab3. Writeanalgebraicexpressiontothegivenverbalexpression. a)eightlessthananumber b)anumberincreasedbyseven

c)anumbersquared d)ninetimesanumber

e)anumberdecreasedbythree f)twolessthanfivetimesanumber g)twiceanumberincreasedbythreetimesthenumber4. Thejuniorgirlsvolleyballteamhasjuststartedtryouts.Writeanexpressionforthenumberofgirlswho

madetheteam.

a)25girlstriedoutfortheteamandthecoachcut13girls 25–13 b)Alotofgirlstriedoutfortheteamandthecoachcut21girls n–21 c)16girlstriedoutfortheteamandthecoachcutsome _________________ d)Somegirlstriedoutfortheteamandthecoachonlycut2 _________________

4

5. Foreachofthefollowing,identifythevariable.Thenwriteanexpression. a)triplethewidthofarectangle b)8yearsyoungerthanVijay c)theareaincreasedby15cm2 d)somepencilssharedequallyamong4students e)doublethelengthdecreasedby6cm f)Sarahboughtsomecoffeefor$1.90each 6. Whatistheexpressionforthenumberofcatsineachexample:

a) ifthereare12dogsinashelterof30animals

b) iftherearexdogsinashelterwith30animals

c) ifthereare11catsinashelterofnanimals

d)iftherearexcatsinaclassofpanimals? 7. Salmagets$12perhourtobaby-sit.Shegetsabonusifshehastobaby-sitpast10p.m.Theexpression

12h+25representswhatSalmawaspaidlastnight.a) Whatisthevariableintheexpression?Explainwhatitrepresentsinreallife.

b)Howmuchdidsheearnlastnight?9.Youhavetopayaone-timefeeof$65tojointhegymplus$2everyclassthatyoutake.Whatisanexpressionforthecostfor“x”classes??2.1Answers1. a)+b)xc)-d)xe)+f)- g)+h)-i)x2. a)7morethananumberb)doubleofanumber c)6lessthananumber d)anumbersquared e)4lessthanthreetimesanumberf)theproductoftwonumbers3. a)n-8 b)n+7 c)n2 d)9n e)n-3 f)5n-2g)2n+3n 4. c)16-x d)x-25. a)Widthofarectangle b)Vijay’sage c)Thearea d)Pencilse)Length f)coffee6. a)30-12n b)30-xc)n-11 d)p-x7. a)Yes.$25b)h.Itrepresentsthenumberofhoursshebaby-sits.c)$858. 56+2x

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MFM1P–Unit2:Algebra–Lesson2 Date:______________Learninggoal:Icansubstituteavalueintoamathexpressionthenevaluate.

2.2Substitution

WARMUP1.Evaluateeachofthefollowing.RemembertouseBEDMAS! a)(4-7)×2+12 b)-10÷5+3×(-4) c)(-5)•6+2•(-7) d)62–4(2+7) 2.Abuilderrentsadigger.Hepaysafixedchargeof$30plus$10perhourtorentthedigger.Workouthowmuchhepaystorentthediggerfor: a)4hours b)8hours c)nhoursAformulaisanexpressionthatusesvariablestoexpressarelationshipbetweentwoormorequantities.Listsomeformulasthatyoualreadyknow…NewVocab

• Substitution

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3.Evaluatethefollowing-replacethevariablewithanumericvalue.-useorderofoperationrulestosimplifytheexpression. a)3x+4y,ifx=7,y=2. b)xy,ifx=6,y=3.

c)

8y+ z ,ifx=3,y=2,z=9. d)3x2–6x,ifx=4

4.Abasketballcourtis20mlongand15mwide.TheperimeterofthecourtisgivenbyP=2l+2wwherelrepresentsthelength,andwrepresentsthewidth.Evaluate(usesubstitution)tofindtheperimeter.5.Youaresavingforaskateboard.Yourauntgivesyou$45tostartandyousave$3eachweek.Theexpression45+3wgivestheamountofmoneyyousaveafterwweeks.Completethetableofvaluestoshowmuchmoneyyouwillhaveovertime.

w 3w+454 8 16 20 24 28

7

6.TheformulatocalculatethepowerforanelectricalcircuitismodeledbytheequationP=i2r,whereirepresentsthecurrentinamperesandrrepresenttheresistanceinohms.Determinethepowerifthecurrentis12amperesandtheresistanceis2ohms.

Homework2.2Substitution1. Evaluateusingthecorrectorderofoperations

a)(-4)-8×(-2)-15 b)(-3)+(-18)÷2÷(-3)

c)(4-7)×2+12 d)-10÷5+3×(-4) d)3×(14–18)–8÷(-4) e)-16÷2×(3+1)2. Evaluateeachexpression a)t+5whent=3 d)3+2ywheny=4 b)d-4whend=7

e) m10

whenm=-30 c)4r-3whenr=-5 f)3x+11whenx=-2

3. Completethetableofvaluesforthefollowingexpressions3x+4.Showyourwork.4. Ifp=4,q=5,andr=-2,whatisthevalueofeachexpression? a)3p+5 b)2q–3 c)4q+r d)pq

5. Describeandcorrecttheerrorinevaluatingtheexpressionwhenm=8.

x 3x+4

-1 3(-1)+4=

0

1

2

3

8

6. Evaluateeachexpressionforthegivenvaluesofthevariables. a)3x2 when

x=2 b)2x2+5x+1 whenx=4

7. TheformulaB=29.95+0.15misusedtocomputethemonthlybillfortheuseofacellularphone.

ComputethevalueofBwhenm=654.

8. Thecostofaschoolbanquetis$65+12n,wherenisthenumberofpeopleattending.Whatisthecostfor62people?

9. Anemployeewhoreceivesaweeklysalaryof$250anda5%commissionispaidaccordingtotheformulap=0.05s+250,whereprepresentsthetotalamountearnedweeklyandsrepresentsthetotalweeklysales.Findtheearningsforaweekwith$2529totalsales.

10. ImaginethatyouownyourownT-shirtbusiness.ThecostofmakingthedesignsandbuyingtheT-shirtsis

$475.Inadditiontotheseonetimecharges,thecostofprintingeachT-shirtis$1.75.Theaveragecost

perT-shirtforthebusinesstomanufacturexT-shirtsismodeledby A = 1.75x + 475x

.Findtheaveragecost

perT-shirtwhenx=100.

11. TheformulaC=23.95d+0.15(m–780)isusedtocomputethecostofrentingacar.Calculatethevalueof

Cwhend=7andm=956.2.2Answers

1. a)-3b)0c)6d)-14e)10f)-322. a)8b)11c)3d)-3e)-23f)53. 4,7,10,134. a)17 b)7c)18d)205. 40+3=436. a)12 b)537. $128.058. $8099. $376.4510. $6.511. $194.05

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Date:______________________

MFM1P–Unit2:Algebra–Lesson3 Date:______________Learninggoal:Iunderstandpolynomialterminologyandcancreatealgebraicexpressions.

2.3AlgebraicExpressions

WARMUPDrawamodeltorepresentx,x2,andx3

StarttofillouttheFISHBONEdiagram(nextpage)withthefollowingdefinitions,usingyournotes:

ü Variable

ü Coefficient

ü Constant

ü LikeTerms

10

11

RepresentingPolynomialsAlgebraTilescanhelpyouvisualizealgebraicexpressions.*shapetellsusthetypeoftile**Colourtellsusthesign(positive/negative)Representthefollowingpolynomialswithalgebratiles

a)3x+1 b)4x2–3x

c) –2x2–2x+4 d)–x2–5NewVocabulary:**ADDTOYOURFISHBONE!

Atermissimplyapartoftheexpression.

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Apolynomialisanalgebraicexpressionmadeof1ormoretermsconnectedbyadditionorsubtraction.

Completethechart.

Expression NumberofTermsName

(monomial,binomial,trinomialorpolynomial?)

4x+3

7a2–2a+5

5x+3y

+2z+4

13

a2+4a-2

6c2–4

NumberofTerms

Typeof

PolynomialExamples Otherexamples

1term

Monomial

57x-3ay2

2terms

Binomial5+x

3x2–2x7a+b

3terms

Trinomial

2x2–3x+5a+b+c

2x+3y–6z

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Homework2.3AlgebraicExpressions*separatesheetofpaper!

1. Modeleachpolynomial. a)3x+2 b)-x2

-2

c)2x2+3–x2. Whatexpressiondoesthemodelshow?

3. SonjaandMyronarediscussingthisalgebratilemodel.

• Sonjasays,“Thismodelshowstheexpression3x2+x+2.”

• Myronsays,“Itshows3x2−x−2.”

a)Whoiscorrect?CircleSONJAorMYRON. b)Give1reasonforyouranswer4. Completethetable

5. Drawouteachofthefollowingexpressions. a) 22 5 3x x− + b) 25 3 2p p− + + c) 25 3 2m m− + +

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6. Whichofthepolynomialsinquestion5canberepresentedbythesamealgebratiles?Explainwhy.

7. Writeanexpressionforeachpolynomial.

8. Explainthemeaningof2tileswiththesameshapebutdifferentcolours.9. Usealgebratilestomodeleachpolynomial.Isthepolynomialamonomial,binomial,ortrinomial?Explain. a) 25x− b) 23 5 6b b− + c) 4 2x−

d)–5+y2 e)–3a2–2a+1 f)v2–4v

10. Forthepolynomial6x–5,statethefollowing:a)numberofterms b)coefficientofthefirstterm c)constantterm11. Explainwhateachofthefollowingwordsmeanusingexamplestohelpwithyourexplanation. a)Binomial b)Coefficient c)Constant d)Term2.3Answers1. a)3Shadedxplus2shaded1 b)oneunshadedx2plustwounshaded1 c)twoshadedx2plusoneunshadedxplusthreeshaded12. -x2-3x+43. a)MYRON. b)Bothshadedandunshadedtilesareintheexpression.4. a)3.Trinomial b)1Monomialc)4Polynomial d)1Monomial5. 6. aandchavethesamealgebratiles.7. a)2x2-3 b)x2-2x+1 c)-x2+3x-2 d)48. Theyaretheoppositeterms.9. a)Monomial b)Trinomial c)Binomial d)Binomiale)Trinomial f)Binomial10. a)2 b)6 c)-511. a)x+ytwotermsconnectedbysubtractionoraddition.b)3xthenumberinfrontofavariablec)6numberd)6xapartoftheexpression

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MFM1P–Unit2:Algebra–Lesson4 Date:______________Learninggoal:Icansimplifyalgebraicexpressionsbycollectingliketerms.

2.4LikeTerms

WARMUP

Whatareliketerms?

• Liketermshavethesamevariable(s)andexponents;onlythecoefficientscanbedifferent.Examples:Example1:Fromthelist,circlethetermsthatarelike2w2.Drawthealgebratilesifneeded

–5w, –6w2, –2, 4w, 3x2, –w2, 7w, 2

Example2:Fromthelist,circlethetermsthatarelike-5x.Drawthealgebratilesifneeded

–4w, –5x2, –6, 5x, 3w2, –x2, 3x, 7

COLLECTINGLIKETERMSMETHOD1:UsingAlgebraTiles 4x–2x+3+6+5x-2 Step1)Drawalgebratilestoshoweachterm. Step2)Groupthetilestoformzeropairs. Step3)Removethezeropairs. Theremainingtilesisyourexpression.

Term Coefficient Variable Exponent6b -3a2 7x c3

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Simplifyeachofthefollowing.(Collectliketerms!) a)2–4m2–8+3m–m2 b)2x2

+3x–1+x2–4x–2

METHOD2:SimplifybyGroupingExample

a) 4+x+1+5x+1 b)2x2+8–11–4x2+5x2

Simplifyeachofthefollowinga) 7d–2d+1–6 b)–4+2a+7–4a

c) 3a2–2a–4+2a–3a2+5 d)–6x2+10x–4+4–12x–7x2

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Homework2.4LikeTerms

1. a)Circlethetermsthatarelike3x: -5x,3x2,3,4x,-11,9x2,-3x,7x,x3

b)Identifytermsthatarelike-2x2: 2x,-3x2,4,-2x,x2,-2,5,3x22. Fillintheblanks.

a)Theoppositeof(+1)_______________.b)Theoppositeofis__________________.c)Addingandproducesaresultof_____________.

3. Combineliketermstowritetheexpressioninitssimplestform.Thefirstoneisdoneforyou.a) =x2-x+3b) =______________ c) =________________d) =__________________4. Combineliketerms.First,rewritetheliketermstogether.Thencombinetheliketerms.Tilescanhelp!

a) -3x+2+x–4 b)6x-3–4x+5=-3x+1x+2–4=-2x–2

c)3x-4+5x+5+4x–5 d)6–3x2+7x2–9

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5. Simplifyeachpolynomialusingamethodofyourchoice.

a) 4+x+1+5x+1 b) –3y2+3y–2c) 2x2+8–11–4x2+5x2 d) 3y+7y2+1–y–2y–3y2

e) 3a2–2a–4+2a–3a2+5 f) 7z–z2+3+z2–7

6. Whichofthefollowingcannotbesimplified?Simplifyonlytheexpressionthatcanbe.Whatdoyou

notice?a) –5y2–3y–4 b) 10x–1c) 1+x–x2 d) 2y2–4–16–7y2–3y+16e) –7+5x–7x–8+14+12x f) 5x2+7+4x–6x2–6–x–2x

7. Writeanexpressionwith5termsthathasonly2termswhenitissimplified.

8. ThefollowingaresomeofTerry’shomeworkanswersthathedidincorrectly.

CirclewherehemademistakesandexplainWHYitiswrong.

Question: 5x2+6x-8+4x-3x2+4

Step1 =5x2-3x2+6x+4x-8+4

Step2 =2x2+10x-4

Step3 =12x3-4

9. Determinetheperimeterofthefollowingfigures.Rememberthatperimeteristhedistancearounda

figure.Showyourworkclearlyandcompletely.Expressyouranswerasapolynomialinsimplifiedform.

2.4Answers

1. a)-5x,4x,-3x,7x b)-3x2,x2,3x22. a)-1 b)shadedx c)0 3. b)x2+3x-3 c)x2+x d)-x2+14. b)2x+2c)12x-4d)4x2-3 5. a)6x+6b)-3y2+3y-2 c)3x2-3 d)4y2+1e)1f)7z-4 6. a)No b)No c)No d)-5y2-3y-4 e)10x-1f)–x2+x+17. 4x-38. a)Step3b)Canonlyaddliketermstogether.9. a)5x+9 b)9x+8

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MFM1P–Unit2:Algebra–Lesson5 Date:______________Learninggoal:Icanaddandsubtractpolynomials.

2.5AddingandSubtractingPolynomials

WARMUPACTIVITY:Usetilesandtwodifferentcolourstorecordyoursolution.Createzeropairsifyouareaddingpositive&negativetiles.Drawthetilesundereachpolynomial&writeanswerinchart.Comparewithneighbor.**comparewithaneighbor.

AddingPolynomials1.Toseparateonepolynomialfromanother,oftenbracketsareused:

Evaluate: USINGTILES: WITHOUTTILES:

2 2(3 5 1) (4 2 )x x x x+ − + −

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2.Writeapolynomialfortheperimeterofthisrectangle.Simplifythepolynomial. SubtractingPolynomialsReview:Subtractingisthesameas______________________the____________________.Thissameideacanbeusedtosubtractpolynomials.Addtheopposite”• Step1:Changethesignandwritetheoppositeofthesecondpolynomial.• Step2:Rewritewithoutthebrackets,groupliketerms,combineliketerms.

Ex.(2x2+3x+5)-(x2+2x+4)

Ex.Trywithouttiles: .

2 2(7 2 13) (4 5 6)b b b b− + − − −

2 1x +

3 7x +

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3.PracticeProblems:Subtract(chooseyourmethod).

a) (4x+2)–(2x+1) b) (4x+2)–(2x–1)

c) (4x+2)–(–2x–1) Bringitalltogether!4.SIMPLIFY.(whatdoesthismean?)

a) (5a2+2a)+(6a2–a) b) (3y2–2y+5)–(–4y2+6y+5)

c) (x2+2x–4)+(4x2–2x–5) d) (–9z2–z–2)–(3z2–z–3)

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Homework2.5AddingandSubtractingPolynomials1. Addeachpolynomial.Usealgebratilesifithelps.

a) (–4h+1)+(6h+3) b) (3y2–2y+5)+(–y2+6y+3) c) (x–5)+(2x+2) d) (y2+6y)+(–7y2+2y)e) (x–5)+(2x+2) f) (b2+3b)+(b2–3b)g) (2a2+a)+(–5a2+3a) h) (3y2–2y+5)+(–y2+6y+3) i) (3–2y+y2)+(–1+y–3y2) j) (5n2+5)+(–1–3n2)

2. Foreachshapebelow,writetheperimeterasasumofpolynomialsandinsimplestform.

i) ii) iii) iv)

3. Thesumoftwopolynomialsis3r2–4r+5.Onepolynomialis2r2+2r–8;whatistheotherpolynomial?

Explainhowyoufoundyouranswer. (_______________________)+(2r2+2r–8)=3r2–4r+54. Subtractthefollowingpolynomials:

a) (2x+3)–(5x+4) b) (4–8w)–(7w+1)

c)(4x+2)–(–2x–1) d) (x2+2x–4)–(4x2+2x–2)

e) (–9z2–z–2)–(3z2–z–3) f) (2s2–3s+6)–(s2–s+2)

5. Astudentsubtracted

a) Explainwhythestudent’ssolutionisincorrect. b)Whatisthecorrectanswer?Showyourwork.

6. Mollyhas(4x+10)dollarsandRonhas(-5x+20)dollars. a)Howmuchmoneydotheyhavealtogether? b)HowmuchmoremoneydoesMollyhavethanRon?

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7. Theperimeterofeachpolygonisgiven.Determineeachunknownlength.

2.5Answers

1. a)2h+4 b)2y2+4y+8 c)3x-3d)-6y2+8ye)3x-3 f)2b2 g)-3a2+4a h)2y2+4y+8 i)-2y2-y+2 j)2n2+4

2. i)6n+6 ii)9p+12 iii)16y+4 iv)2a+233. r2-6r+134. a)-3x-1 b)3-15w c)6x+3d)-3x2-2 e)-6z2+1 f)s2-2s+45. a)-5x2since-2-3=-5.b)-5x2-x+126. a)x+30 b)9x-107. a)w+4b)s+3

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MFM1P–Unit2:Algebra–Lesson6 Date:______________Learninggoal:Icanusethedistributivepropertytomultiplyanumberandapolynomial.

2.6TheDistributiveProperty-Part1

Think…Whenyoudistributesomethingyougivethatthingtoeachpersoninagroup.TheDistributiveLawIfyoumultiplyanumberbyabracket,thenmultiplyeachterminthebracketbythatnumber.Wecallthis“EXPANDING”NewVocab:

ExpandàExample1:Expandthefollowing.a) 3(x+2) b)2(4r–4)= c) (3n+6)(4)d)2(x+3)

e)(2–n)(8) f)4(y+2)

DISTRIBUTINGANEGATIVEcanbeTRICKY!BECAREFULWITHYOURNEGATIVES!Examples2:Expandthefollowing. a)-5(n+4)

b)–(4–y) c)(7m–5)(-3)

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Sometimesyouneedtodistributethencollectliketerms.Examples3:Fullysimplifyeachofthefollowing. a) 2(6x–4)+x b) 4–2(m+5) Distribute_________ Distribute________________ Simplify. Simplify.‘

c)15t–(t-4) d)-6(v+1)+vAPPLICATIONSExample4:Writeasimplifiedexpressionfortheareaofthefollowingrectangles

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Homework2.6TheDistributiveProperty–Part11. Fullysimplifyeachofthefollowing.

a) 4(3a+2) b) (d2+2d)(–3) c)2(4c2–2c+3) d) (–2n2+n–1)(6) e) –3(–5m2+6m+7) f)(5t2–2t)(–9)g) 3(x2+x–4) h)2(m2–3m+5) i)–4(b2–2b–3) j)5(c2–6c–1) k)–3(4–h2) l ) (n2+4n+3)(–2) g)(5t2–2t)(–3) h)(w2+2w–5)(4) h)–(4x2–3x–5)

2. Hereisastudent’ssolutionforthisquestion:

a)Explainwhythestudent’ssolutionisincorrect. b)Whatisthecorrectanswer?Showyourwork.(Thestudentmade2errors!!)3. UsetheDistributivePropertytowriteandsimplifyanexpressionfortheareaoftherectangle.a) b) c)4. ExpandandSimplify a) ( ) ( )5332 ++− xx b) ( ) ( )1243 +−− kk c)5 j −3( )−3 j −3( ) d)3 y− 2( )+ 2 4− 2y( )+ 6− 7y( )

e) ( ) ( ) ( )543234 22 −−+−−− kkkk f) ( ) ( )baba +−− 52234 5. Acomputerrepairtechniciancharges$50pervisitplus$30/hourforhousecalls. a)Writeanalgebraicexpressionthatdescribestheservicechargeforonehouseholdvisit. b)Useyourexpressiontofindthetotalservicechargefora2.5hourrepairjob. c)Supposeallchargesaredoubledforholidays.Writeasimplifiedexpressionfortheseservicecharges onaholiday. d)Useyoursimplifiedexpressionfrompartc)tocalculatethecostfora2.5hourrepairjobona holiday.

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2.6Answers1. a)12a+8b)-3d2-6dc)8c2-4c+6d)-12n2+6n-6e)15m2-18m-21f)-45t2+18tg)3x2+3x-12h)2m2-6m+10i)-4b2+8b+12 j)5c2-30c-5 k)-12+3h2 l)-2n2-8n-6m)-15t2+6tn)4w2+8w-20o)-4x2+3x+52. a)2rand-14b)-8r2+2r-143. a)91-13x b)14x+35c)8x+644. a)5x+9 b)k-14 c)2j-6 d)-8y+8 e)-3k2+10k-15 f)2a-10b5. a)C=50+30hb)$125c)100+60hd)$250

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MFM1P–Unit2:Algebra–Lesson7 Date:______________Learninggoal:Icanusethedistributivepropertytomultiplytwopolynomials.

2.7TheDistributiveProperty-Part2

WARMUP.HowwouldwemodelMULTIPLYINGwithtiles?Steps

1. Usetilestomodeleachexpressiononthesidesofarectangle.2. Fillintheareaoftherectangleusingtiles.Rememberyoursign

rulesformultiplication….seechartà3. Countthetilesinsidethearea.Writethisbycollectingliketerms.

1.Examplestogetuswarmedup…a) b)2(4) -3(4)

Answer:=________ Answer:=________Nowtrysomeexamplesusingvariables(letters)…c) d)3(2x) –3x(4)

Answer:=________ Answer:=________

Sign rules for multiplying:

29

e)(3x)(2x) f)(-4x)(2x)

Answer:=________ Answer:=________Whataboutletterswithexponents?Like(x2)(x3)or(x2)(x)?Wecannotuseareamodelsforthese.Let’slearnhowtodothiswithouttiles…..2.Practice:Multiplyeachofthefollowingmonomials.*therearerulesforexponents!!

a)(-3x2)(7x) b)(2x2)(-3x) c)(-3x)(-12x)

Whenmultiplyingthesamevariables(letters),you___________the______________________.3.Whatifthereare2termsinbracket?

Simplify:3x(2x+4).

Method1(tiles): Method2(notiles):

30

Simplifya)2a(5a+3) b)4b(3b−2) c)−3c(−5c-1)

4.Jacobisdesigningapoolandadeckthatwillsoundthepool.Hehassketchedthefollowing.

a) Determinetheareaofthepool

b) Determinetheareaofthedeck(withoutthepool)

31

Assignment2.7DistributionPart21.Simplify

a)(x)(3x) b)(x)(5x) c)(3x)(5x) d)(7x)(2x)

e)(x2)(x) f)(3x)(3x2) g)(12x)(3x2) h)(6x)(6x2)

2. Multiply.

a)(-3)(2x) b)(2x)(-9) c)(4x)(-4) d)(5)(-2x)

e)(8)(-x) f)(5x)(-7) g)(-9x)(9) h)(-3x)(-6)

i)(2x2)(-3x) j)(4x2)(-8x) k)(-3x)(4x2) l)(2x)(-2x2)

3. Thisdiagramshowsonerectangleinsideanother.a) Determinetheareaofthesmallandbigrectangle.

b) Determinetheareaoftheshadedregion.4. Astudentthinksthattheproduct2x(x+1)is2x2+1.Chooseamodel.Usethemodeltoexplainhowtoget

thecorrectanswer.5. Determineeachproduct(multiply) a)2x(x–6) b)3t(5t+2) c)2w(3w–5) d)-3g(5–g)

32

6. Simplify a)3(x2

+x–4) b)–4(b2

–2b–3) c)–3h(4–h2)

d)(5t2

–2t)(–t) e)-x(2+8x) f)(4+3y)(-2y)

g)2(m2–3m+5) h)5c(2c2–6c–1)

7. AnL-shapedpatioisbuiltfromtworectangularareasAandB. a)Writeasimplifiedexpressionforthetotalareaofthepatio.

b)Findthetotalareaofthepatiowhenxis3m.

2.7Answers1. a)3x2 b)5x2 c)15x2 d)14x2 e)x3 f)9x3 g)36x3h)36x32. a)-6x b)-18x c)-16x d)-10x e)-8xf)-35x g)-81xh)18x

i)-6x3 j)-32x3 k)-12x3 l)-4x33. a)Large=18x2,Small=8x2b)10x2,Subtracttheareaofthesmallrectanglefromtheareaofthelargerectangle.4. 2x*x=2x2 2x*1=2xCorrectanswer:2x2+2x5. a)2x2-12x b)15t2+6t c)6w2-10w d)3g2-15g6. a)3x2+3x-12 b)-4b2+8b+12 c)3h3-12hd)-5t3+2t2e)-8x2-2xf)-6y2-8yg)2m2-6m+10h)10c3-30c2-5c 7. a)4x2+15x-5b)76m2