# You notice that a certain rule is repeated three

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Younoticethatacertainruleisrepeatedthreetimestodistributethefirstpolynomialoverthesecondpolynomial.Then,theexpressionobtainedineachstepcanbeexpandedusingthealgorithmicmethod.TheexpressionfromtheStep1:x(ab+bc+ac)=xab+4.xismultipliedbythefirsttermofthesecondpolynomialxbc+5.xismultipliedbythesecondtermofthesecondpolynomialxac6.xismultipliedbythefirsttermofthesecondpolynomialApplyingSteps46totheexpressionsobtainedinSteps2and3,weget:7.y(ab+bc+ac)=yab+ybc+yac8.z(ab+bc+ac)=zab+zbc+zacFinally,wecanputtogetherallthedistributionsfromSteps48,tofindtheoutcomeoftheproductoftwopolynomialsasfollows:(x+y+z)(ab+bc+ac+abc)=xab+xbc+xac+yab+ybc+yac+zab+zbc+zacApplyingConceptsandPrinciples:Sometimeswhensolvingaproblemwedonothaveawelldefinedalgorithm,aformula,oracertainmethod.Butwecanputsomeofthesemethodsanddifferentconceptsandprinciplestogethertobuildasolutionprocessfortheproblem.Forexample:AssumethatD=180(n ‒ 2)isthesumofalltheinterioranglesofaregularpolygonwithnsides.Now,weincreasethenumberofthesidesby7,andwanttoknowthathowmuchthesumoftheinterioranglesinthenewpolygonismorethantheoriginalone.Wedonothaveanalgorithmoraparticularformulatofindsuchanincrease.Ratherwecanusetheconceptofthevariationinanequation.Let’ssayD1=SumoftheinterioranglesoftheoriginalpolygonD2=Sumoftheinterioranglesofthenewpolygonwith7moresides.Then,D1=180(n ‒ 2)=180n ‒ 360Now,wemustreplacenwith(n+7)
PERT - A Math Study GuideAllRightsReservedD2=180[(n+7) ‒ 2]=180(n+5)=180n+900Next,subtractD1fromD2tofindtheincreaseD2 ‒ D1=(180n+900) ‒ (180n ‒ 360)=180n+900 ‒ 180n+360=900+360=1260degreesincrease13. Translate between Lines and EquationsAsyouseesomesamplepointsonthecoordinateplanebelow,thereareinfinitenumberofsuchpointsonacoordinateplane.Eachpointisidentifiedbytwodistances:DistancefromthehorizontalaxisorthexaxisDistancefromtheverticalaxisortheyaxis.Forexample,thedistanceofthepointAfromxaxisis5andfromyaxisis ‒4ThesedistancesarecalledthecoordinatesofthepointAandaredenotedby(4,5)

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