boards concepts booster algebraic ......4 concept for boards || chapter algebraic expressions and...

BOARDSCONCEPTSBOOSTER

ALGEBRAICEXPRESSIONSANDIDENTITIES

DownloadDoubtnutToday

QuesNo. Question

1

CONCEPT FOR BOARDS || Chapter ALGEBRAIC EXPRESSIONS ANDIDENTITIES

1.INTRODUCTIONTOALGEBRA

1.Introduction

ClicktoLEARNthisconcept/topiconDoubtnut

2

1.INTRODUCTION

1.Introduction

3

2.POLYNOMIALS

1.polynomialsanalgebraicexpressioninwhichthevariablesinvolvedhaveonlynon-negativeintegralpowersiscalledapolynomial.

https://doubtnut.app.link/TcKENhKmIQ

https://doubtnut.app.link/DtqAZDWxIQ?$fallback_url=https%3A%2F%2Fdoubtnut.com%2Fvideo%2Fdefault%2Fdefault%2FMTUyODM3OA%3D%3D

https://doubtnut.app.link/Qer4LHWxIQ?$fallback_url=https%3A%2F%2Fdoubtnut.com%2Fvideo%2Fdefault%2Fdefault%2FMTUyODMyNA%3D%3D

https://doubtnut.app.link/CUzSoLWxIQ?$fallback_url=https%3A%2F%2Fdoubtnut.com%2Fvideo%2Fdefault%2Fdefault%2FMTUyODM3OQ%3D%3D

4

2.REVIEWOFCONCEPTSANDDEFINITIONS

1.ConstantAsymbolhavingafixednumericalvalueiscalledaconstant.

5

2.POLYNOMIALS

2.Degreeofapolynomialinonevariableinapolynomialinonevariablethehighestpowerofthevariableiscalleditsdegree.

6

2.variableAsymbolwhichtakesvariousnumericalvaluesiscalledavariable.

7

2.POLYNOMIALS

3.Degreeofapolynomial in twovariable inapolynomial inmore thanonevariabletheofsumofthepowersofthevariableineachtermiscomputedsumosobtainediscalledthedegreeofthepolynomial.

https://doubtnut.app.link/eF5K4MWxIQ?$fallback_url=https%3A%2F%2Fdoubtnut.com%2Fvideo%2Fdefault%2Fdefault%2FMTUyODMyNQ%3D%3D

https://doubtnut.app.link/voKxLQWxIQ?$fallback_url=https%3A%2F%2Fdoubtnut.com%2Fvideo%2Fdefault%2Fdefault%2FMTUyODM4MA%3D%3D

https://doubtnut.app.link/sjSlFSWxIQ?$fallback_url=https%3A%2F%2Fdoubtnut.com%2Fvideo%2Fdefault%2Fdefault%2FMTUyODMyNg%3D%3D

https://doubtnut.app.link/zMh8CUWxIQ?$fallback_url=https%3A%2F%2Fdoubtnut.com%2Fvideo%2Fdefault%2Fdefault%2FMTUyODM4MQ%3D%3D

8

3.AlgebraicexpressionsAcombinationofconstantsandvariablesconnectedbythesignsof fundamental operationsof addition subtractionmultiplicationanddivision iscalledanalgebraicexpression.

9

2.POLYNOMIALS

4.Constantpolynomialapolynomialconsistingofaconstanttermiscalledaconstantpolynomial.thedegreeofaconstantpolynomialiszero.

10

4.TermsVariouspartsofanalgebraicexpressionwhichareseparatedbythesignsof+or-arecalledthetermsoftheexpression.

11

2.POLYNOMIALS

5.Linearpolynomialapolynomialofdegree1iscalledalinearpolynomial.

https://doubtnut.app.link/BjulyWWxIQ?$fallback_url=https%3A%2F%2Fdoubtnut.com%2Fvideo%2Fdefault%2Fdefault%2FMTUyODMyNw%3D%3D

https://doubtnut.app.link/lqk4BYWxIQ?$fallback_url=https%3A%2F%2Fdoubtnut.com%2Fvideo%2Fdefault%2Fdefault%2FMTUyODM4Mg%3D%3D

https://doubtnut.app.link/hzQ6o2WxIQ?$fallback_url=https%3A%2F%2Fdoubtnut.com%2Fvideo%2Fdefault%2Fdefault%2FMTUyODMyOA%3D%3D

https://doubtnut.app.link/CdQBi4WxIQ?$fallback_url=https%3A%2F%2Fdoubtnut.com%2Fvideo%2Fdefault%2Fdefault%2FMTUyODM4Mw%3D%3D

12

5.MonomialAnalgebraicexpressioncontainingonlyonetermiscalledamonomial.

13

2.POLYNOMIALS

6.Quadraticpolynomialapolynomialofdegree2iscalledaquadraticpolynomial

14

6.BinomialAnalgebraicexpressioncontainingtwotermsiscalledabinomial.

15

2.POLYNOMIALS

7.Cubicpolynomialofdegree3iscalledancubicpolynomial

https://doubtnut.app.link/ccLL05WxIQ?$fallback_url=https%3A%2F%2Fdoubtnut.com%2Fvideo%2Fdefault%2Fdefault%2FMTUyODMyOQ%3D%3D

https://doubtnut.app.link/OcTRU7WxIQ?$fallback_url=https%3A%2F%2Fdoubtnut.com%2Fvideo%2Fdefault%2Fdefault%2FMTUyODM4NA%3D%3D

https://doubtnut.app.link/1NZUBbXxIQ?$fallback_url=https%3A%2F%2Fdoubtnut.com%2Fvideo%2Fdefault%2Fdefault%2FMTUyODMzMA%3D%3D

https://doubtnut.app.link/nwtAhfXxIQ?$fallback_url=https%3A%2F%2Fdoubtnut.com%2Fvideo%2Fdefault%2Fdefault%2FMTUyODM4NQ%3D%3D

16

7.TrinomialAnalgebraicexpressioncontainingthreetermsiscalledatrinomial.

17

2.POLYNOMIALS

8.Biquadraticpolynomialapolynomialofdegree4iscalledabiquadraticpolynomial.

18

8.FACTORS

19

9.CoefficientInatermofanalgebraicexpressionanyofthefactorswiththesignofthetermiscalledthecoefficientoftheproductoftheotherfactors.

https://doubtnut.app.link/2eVechXxIQ?$fallback_url=https%3A%2F%2Fdoubtnut.com%2Fvideo%2Fdefault%2Fdefault%2FMTUyODMzMQ%3D%3D

https://doubtnut.app.link/acF61kXxIQ?$fallback_url=https%3A%2F%2Fdoubtnut.com%2Fvideo%2Fdefault%2Fdefault%2FMTUyODM4Ng%3D%3D

https://doubtnut.app.link/yHOQRpXxIQ?$fallback_url=https%3A%2F%2Fdoubtnut.com%2Fvideo%2Fdefault%2Fdefault%2FMTUyODMzMg%3D%3D

https://doubtnut.app.link/Xr6BPrXxIQ?$fallback_url=https%3A%2F%2Fdoubtnut.com%2Fvideo%2Fdefault%2Fdefault%2FMTUyODMzMw%3D%3D

20

10.ConstanttermAtermoftheexpressionhavingnoliteralfactoriscalledaconstantterm.

21

11.LikeandunliketermsThetermshavingthesameliteralfactorsarecalledlikeorsimilartermsotherwisetheyarecalledunliketerms.

22

3.DIVISIONOFAMONOMIALBYAMONOMIAL

1.Divisionofamonomialbyamonomial

23

3.ALGEBRAICEXPRESSIONS

1.Additionofalgebraicexpressionswithexamples

https://doubtnut.app.link/BAPx9tXxIQ?$fallback_url=https%3A%2F%2Fdoubtnut.com%2Fvideo%2Fdefault%2Fdefault%2FMTUyODMzNA%3D%3D

https://doubtnut.app.link/68UzkzXxIQ?$fallback_url=https%3A%2F%2Fdoubtnut.com%2Fvideo%2Fdefault%2Fdefault%2FMTUyODMzNQ%3D%3D

https://doubtnut.app.link/n4DP7AXxIQ?$fallback_url=https%3A%2F%2Fdoubtnut.com%2Fvideo%2Fdefault%2Fdefault%2FMTUyODM4Nw%3D%3D

https://doubtnut.app.link/eZwLPEXxIQ?$fallback_url=https%3A%2F%2Fdoubtnut.com%2Fvideo%2Fdefault%2Fdefault%2FMTUyODMzNg%3D%3D

24

3.ALGEBRAICEXPRESSIONS

2.Subtractionofalgebraicexpressionswithexamples.

25

4.MULTIPLICATIONOFALGEBRAICEXPRESSIONS

1.MultiplyingTwoMonomials.

26

4.ALGEBRAICEXPRESSIONSWHICHARENOTPOLYNOMIALS

1.Algebraicexpressionswhicharenotpolynomials

https://doubtnut.app.link/RYoKEGXxIQ?$fallback_url=https%3A%2F%2Fdoubtnut.com%2Fvideo%2Fdefault%2Fdefault%2FMTUyODMzNw%3D%3D

https://doubtnut.app.link/sxvapIXxIQ?$fallback_url=https%3A%2F%2Fdoubtnut.com%2Fvideo%2Fdefault%2Fdefault%2FMTUyODMzOA%3D%3D

https://doubtnut.app.link/iA1brKXxIQ?$fallback_url=https%3A%2F%2Fdoubtnut.com%2Fvideo%2Fdefault%2Fdefault%2FMTUyODM4OA%3D%3D

https://doubtnut.app.link/hBTqiMXxIQ?$fallback_url=https%3A%2F%2Fdoubtnut.com%2Fvideo%2Fdefault%2Fdefault%2FMTUyODMzOQ%3D%3D

2.RULE1Thecoefficientoftheproductsoftwomonomialsisequaltotheproductsoftheircoefficients.

28

3.RULE2Thevariablepartintheproductsoftwomonomialsisequaltotheproductofthevariablepartsinthegivenmonomials.

29

4.Multiplicationofamonomialandabinomial

30

5.MULTIPLICATIONOFTWOBINOMIALS

1.(1)ColumnMethod

https://doubtnut.app.link/hBTqiMXxIQ?$fallback_url=https%3A%2F%2Fdoubtnut.com%2Fvideo%2Fdefault%2Fdefault%2FMTUyODMzOQ%3D%3D

https://doubtnut.app.link/fDdowOXxIQ?$fallback_url=https%3A%2F%2Fdoubtnut.com%2Fvideo%2Fdefault%2Fdefault%2FMTUyODM0MA%3D%3D

https://doubtnut.app.link/U6tLoQXxIQ?$fallback_url=https%3A%2F%2Fdoubtnut.com%2Fvideo%2Fdefault%2Fdefault%2FMTUyODM0MQ%3D%3D

https://doubtnut.app.link/AyKwcVXxIQ?$fallback_url=https%3A%2F%2Fdoubtnut.com%2Fvideo%2Fdefault%2Fdefault%2FMTUyODM0Mg%3D%3D

31

5.DIVISIONOFPOLYNOMIALINONEVARIABLE

1.Divisionofapolynomialbyamonomial

32

5.MULTIPLICATIONOFTWOBINOMIALS

2.Multiply: 2x2 - 3x + 5 by(5x + 2).

33

2.Divisionofapolynomialbyabinomialbyusinglongdivision

34

3.Divisionalgorithmforpolynomials

( )

https://doubtnut.app.link/G6W7s1XxIQ?$fallback_url=https%3A%2F%2Fdoubtnut.com%2Fvideo%2Fdefault%2Fdefault%2FMTUyODM4OQ%3D%3D

https://doubtnut.app.link/hAoGB3XxIQ?$fallback_url=https%3A%2F%2Fdoubtnut.com%2Fvideo%2Fdefault%2Fdefault%2FMTUyODM0Mw%3D%3D

https://doubtnut.app.link/mcGVu5XxIQ?$fallback_url=https%3A%2F%2Fdoubtnut.com%2Fvideo%2Fdefault%2Fdefault%2FMTUyODM5MA%3D%3D

https://doubtnut.app.link/usTqo7XxIQ?$fallback_url=https%3A%2F%2Fdoubtnut.com%2Fvideo%2Fdefault%2Fdefault%2FMTUyODM5MQ%3D%3D

https://doubtnut.app.link/KmHMk9XxIQ?$fallback_url=https%3A%2F%2Fdoubtnut.com%2Fvideo%2Fdefault%2Fdefault%2FMTUyODM5Mg%3D%3D

4.Analternativeandshorterformoflongdivision

36

6.IDENTITIES

1.IDENTITY:Anidentityisanequalitywhichistrueforallvaluesofthevariables.

37

6.DIVISIONOFPOLYNOMIALBYUSINGFACTORIZATION

1.Divisionofpolynomialbyusingfactorization

38

6.IDENTITIES

2.Toverifythealgebraicidentity[a + b]2 = a2 + 2ab + b2

6.IDENTITIES

https://doubtnut.app.link/KmHMk9XxIQ?$fallback_url=https%3A%2F%2Fdoubtnut.com%2Fvideo%2Fdefault%2Fdefault%2FMTUyODM5Mg%3D%3D

https://doubtnut.app.link/cual8aYxIQ?$fallback_url=https%3A%2F%2Fdoubtnut.com%2Fvideo%2Fdefault%2Fdefault%2FMTUyODM0NA%3D%3D

https://doubtnut.app.link/g9sERcYxIQ?$fallback_url=https%3A%2F%2Fdoubtnut.com%2Fvideo%2Fdefault%2Fdefault%2FMTUyODM5Mw%3D%3D

https://doubtnut.app.link/sk29LfYxIQ?$fallback_url=https%3A%2F%2Fdoubtnut.com%2Fvideo%2Fdefault%2Fdefault%2FMTUyODM0NQ%3D%3D

https://doubtnut.app.link/gBvpJjYxIQ?$fallback_url=https%3A%2F%2Fdoubtnut.com%2Fvideo%2Fdefault%2Fdefault%2FMTUyODM0Ng%3D%3D

39 3.Provethat:(a - b)2 = a2 - 2ab + b2

40

6.IDENTITIES

4.ImportantIdentity-(a - b)(a + b) = a2 - b2(ii)(x + a)(x + b) = x2 + (a + b)x + ab

41

6.IDENTITIES

5.EVALUATE:(i)(2x + 3y)2(ii)(2x - 3y)2(iii)(2x + 3y)(2x - 3y)

42

6.IDENTITIES

6.Ifx +1x= 4;Find(i)x2 +

1

x2(ii)x4 +

1

x4

https://doubtnut.app.link/gBvpJjYxIQ?$fallback_url=https%3A%2F%2Fdoubtnut.com%2Fvideo%2Fdefault%2Fdefault%2FMTUyODM0Ng%3D%3D

https://doubtnut.app.link/GKB9MlYxIQ?$fallback_url=https%3A%2F%2Fdoubtnut.com%2Fvideo%2Fdefault%2Fdefault%2FMTUyODM0Nw%3D%3D

https://doubtnut.app.link/2X7NHnYxIQ?$fallback_url=https%3A%2F%2Fdoubtnut.com%2Fvideo%2Fdefault%2Fdefault%2FMTUyODM0OA%3D%3D

https://doubtnut.app.link/pbvxxsYxIQ?$fallback_url=https%3A%2F%2Fdoubtnut.com%2Fvideo%2Fdefault%2Fdefault%2FMTUyODM0OQ%3D%3D

https://doubtnut.app.link/JxJ9FwYxIQ?$fallback_url=https%3A%2F%2Fdoubtnut.com%2Fvideo%2Fdefault%2Fdefault%2FMTUyODM1MA%3D%3D

436.IDENTITIES

7.Ifx -1x= 9findx2 +

1

x2.

44

6.IDENTITIES

8.Ifx + y = 12 and xy = 14findthevaluesofx2 + y2.

45

6.IDENTITIES

9.Usingtheformulaforsquaringabinomialevaluatethefollowing(i)(101)2 (ii)(99)2

(iii)(93)2

46

6.IDENTITIES

10.Whatmustbeaddedto9x2 - 24x + 10tomakeitawholesquare?

https://doubtnut.app.link/JxJ9FwYxIQ?$fallback_url=https%3A%2F%2Fdoubtnut.com%2Fvideo%2Fdefault%2Fdefault%2FMTUyODM1MA%3D%3D

https://doubtnut.app.link/b4yOAyYxIQ?$fallback_url=https%3A%2F%2Fdoubtnut.com%2Fvideo%2Fdefault%2Fdefault%2FMTUyODM1MQ%3D%3D

https://doubtnut.app.link/IGHwrCYxIQ?$fallback_url=https%3A%2F%2Fdoubtnut.com%2Fvideo%2Fdefault%2Fdefault%2FMTUyODM1Mg%3D%3D

https://doubtnut.app.link/z51ycGYxIQ?$fallback_url=https%3A%2F%2Fdoubtnut.com%2Fvideo%2Fdefault%2Fdefault%2FMTUyODM1Mw%3D%3D

https://doubtnut.app.link/cfkG0HYxIQ?$fallback_url=https%3A%2F%2Fdoubtnut.com%2Fvideo%2Fdefault%2Fdefault%2FMTUyODM1NA%3D%3D

477.ASPECIALPRODUCT

1.ImportantIdentitiy(x + a)(x + b) = x2 + (a + b)x + ab

48

7.ASPECIALPRODUCT

2.Evaluatethefollowing:(i)107 × 103(ii)56 × 48(iii)95 × 97

49

8.ACTIVITIESFORVERIFYINGTHEIDENTITIES

1.Toverifythealgebraicidentity[a + b]2 = a2 + 2ab + b2

50

2.Verificationofidentity(a-b)^2

51

3.ImportantIdentity-(a - b)(a + b) = a2 - b2(ii)(x + a)(x + b) = x2 + (a + b)x + ab

https://doubtnut.app.link/cfkG0HYxIQ?$fallback_url=https%3A%2F%2Fdoubtnut.com%2Fvideo%2Fdefault%2Fdefault%2FMTUyODM1NA%3D%3D

https://doubtnut.app.link/cNx0FJYxIQ?$fallback_url=https%3A%2F%2Fdoubtnut.com%2Fvideo%2Fdefault%2Fdefault%2FMTUyODM1NQ%3D%3D

https://doubtnut.app.link/yTRSpLYxIQ?$fallback_url=https%3A%2F%2Fdoubtnut.com%2Fvideo%2Fdefault%2Fdefault%2FMTUyODM1Ng%3D%3D

https://doubtnut.app.link/K6RYlPYxIQ?$fallback_url=https%3A%2F%2Fdoubtnut.com%2Fvideo%2Fdefault%2Fdefault%2FMTUyODM1Nw%3D%3D

https://doubtnut.app.link/DrGEkTYxIQ?$fallback_url=https%3A%2F%2Fdoubtnut.com%2Fvideo%2Fdefault%2Fdefault%2FMTUyODM1OA%3D%3D

52

4.ImportantIdentitiy(x + a)(x + b) = x2 + (a + b)x + ab

DownloadDoubtnuttoAskAnyMathQuestionByjustaclick

GetAVideoSolutionForFreeinSeconds

DoubtnutHasMoreThan1LakhVideoSolutions

Free Video Solutions of NCERT, RD Sharma, RS Aggarwal, Cengage(G.Tewani), Resonance DPP, Allen, Bansal, FIITJEE, Akash, Narayana,VidyaMandir

DownloadDoubtnutToday

https://doubtnut.app.link/DrGEkTYxIQ?$fallback_url=https%3A%2F%2Fdoubtnut.com%2Fvideo%2Fdefault%2Fdefault%2FMTUyODM1OA%3D%3D

https://doubtnut.app.link/yTtaPZYxIQ?$fallback_url=https%3A%2F%2Fdoubtnut.com%2Fvideo%2Fdefault%2Fdefault%2FMTUyODM1OQ%3D%3D

boards concepts booster algebraic ......4 concept for boards || chapter algebraic expressions and...

Documents

we welcomed m.c. escher in turkey’s new geometry...

inequalities algebraic concepts and applications

math vocabulary algebraic concepts m5.d aligning with...

handbook of mathematics - hdbom.com · algebraic complex...

incidence geometry from an algebraic graph theory point of...

p6 dash boards concepts

an algebraic oak - algebraic poem

1 strategies for accessing algebraic concepts (k-8) access...

resultants: algebraic and di erential · we will review the...

teachers’ resource manual - apsacssectt.edu.pk...

unit and lesson plan matthew carroll second grade math...

stability concepts in algebraic geometry · this thesis...

1wseaman/smarts/eop-smarts-report... · web viewnbr. sense,...

math unit22 algebraic concepts

diﬀerential algebraic topology -...

algebraic homogeneous spaces of algebraic groups

chapter 1 algebraic numbers and algebraic integers...chapter...

geometric models for algebraic concepts gregg velatini...

algebraic fractions algebraic fractions simplify rational...

multigrid methods algebraic multigrid methods algebraic...