christine crisp每本级数学卷核心模块二项式展开介绍.pptx

christine crisp每本级数学卷核心模块二项式展开介绍.pptx

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45:EvenMoreBinomial Expansions?ChristineCrisp“TeachALevelMaths”

Vol.2:A2CoreModules

ModuleC4Certainimagesand/orphotosonthispresentationarethecopyrightedpropertyofJupiterImagesandarebeingusedwithpermissionunderlicense.Theseimagesand/orphotosmaynotbecopiedordownloadedwithoutpermissionfromJupiterImages

Thebinomialexpansioncanalsobeusedwithalgebraicfractions.Solution:WejustwritetheexpressionasOnlythe2ndfactorneedsexpanding.e.g.Findtheexpansioninascendingpowersofx,uptoandincludingtheterm,forthefollowingandgivethevaluesofxforwhichtheexpansionisvalid.

So,Replacenbyandxby(3x)

StartwithWedon’tneedanytermswithpowershigherthan.

thenStartwithWedon’tneedanytermswithpowershigherthan.

thenStartwithfinallyWedon’tneedanytermswithpowershigherthan.

thenStartwithfinallyWedon’tneedanytermswithpowershigherthan.

So,ValidforWedon’tneedanytermswithpowershigherthan.

ExercisesFindthe1st4terms,intheexpansioninascendingpowersofx,forthefollowingandgivethevaluesofxforwhichtheexpansionisvalid.

Solution:Replacenbyandxby(-x)

Solution:So,Validfor

Theexpressionswe’veusedinbinomialexpansionshaveallbeenoftheformThe1sttermis1,andthisistheONLYformwecanuse.Anyotherexpressionswewanttoexpandmustbewrittenwith1asthe1stterm.Toexpandforexamplewemustremove4fromthebrackets.

WewriteWhilstthe4isinsidethebracketsitisincludedunderthepowerso,whenwetakethe4outside,acopyofthepowermustcomewithit.

WewriteThe4outsidethebracketsmultipliesbothtermsinside,sothe2ndtermmustbedividedby4.

WewriteWenowexpandasbefore,rememberingtomultiplyby2.

Thereisn’taconvenientplacetoputthe2!soIwriteitastoavoidpilingupthefractions.ReplacenbyandxbyValidfor

SUMMARYToexpande

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