BOARDS CONCEPTS BOOSTER ALGEBRAIC ......4 CONCEPT FOR BOARDS || Chapter ALGEBRAIC EXPRESSIONS AND...

BOARDSCONCEPTSBOOSTER

ALGEBRAICEXPRESSIONSANDIDENTITIES

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CONCEPT FOR BOARDS || Chapter ALGEBRAIC EXPRESSIONS ANDIDENTITIES

1.INTRODUCTIONTOALGEBRA

1.Introduction

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1.INTRODUCTION

1.Introduction


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2.POLYNOMIALS

1.polynomialsanalgebraicexpressioninwhichthevariablesinvolvedhaveonlynon-negativeintegralpowersiscalledapolynomial.


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2.REVIEWOFCONCEPTSANDDEFINITIONS

1.ConstantAsymbolhavingafixednumericalvalueiscalledaconstant.


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2.POLYNOMIALS

2.Degreeofapolynomialinonevariableinapolynomialinonevariablethehighestpowerofthevariableiscalleditsdegree.


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2.variableAsymbolwhichtakesvariousnumericalvaluesiscalledavariable.


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2.POLYNOMIALS

3.Degreeofapolynomial in twovariable inapolynomial inmore thanonevariabletheofsumofthepowersofthevariableineachtermiscomputedsumosobtainediscalledthedegreeofthepolynomial.


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3.AlgebraicexpressionsAcombinationofconstantsandvariablesconnectedbythesignsof fundamental operationsof addition subtractionmultiplicationanddivision iscalledanalgebraicexpression.


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2.POLYNOMIALS

4.Constantpolynomialapolynomialconsistingofaconstanttermiscalledaconstantpolynomial.thedegreeofaconstantpolynomialiszero.


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4.TermsVariouspartsofanalgebraicexpressionwhichareseparatedbythesignsof+or-arecalledthetermsoftheexpression.


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2.POLYNOMIALS

5.Linearpolynomialapolynomialofdegree1iscalledalinearpolynomial.



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5.MonomialAnalgebraicexpressioncontainingonlyonetermiscalledamonomial.


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2.POLYNOMIALS

6.Quadraticpolynomialapolynomialofdegree2iscalledaquadraticpolynomial


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6.BinomialAnalgebraicexpressioncontainingtwotermsiscalledabinomial.


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2.POLYNOMIALS

7.Cubicpolynomialofdegree3iscalledancubicpolynomial




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7.TrinomialAnalgebraicexpressioncontainingthreetermsiscalledatrinomial.


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2.POLYNOMIALS

8.Biquadraticpolynomialapolynomialofdegree4iscalledabiquadraticpolynomial.


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8.FACTORS


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9.CoefficientInatermofanalgebraicexpressionanyofthefactorswiththesignofthetermiscalledthecoefficientoftheproductoftheotherfactors.




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10.ConstanttermAtermoftheexpressionhavingnoliteralfactoriscalledaconstantterm.


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11.LikeandunliketermsThetermshavingthesameliteralfactorsarecalledlikeorsimilartermsotherwisetheyarecalledunliketerms.


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3.DIVISIONOFAMONOMIALBYAMONOMIAL

1.Divisionofamonomialbyamonomial


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3.ALGEBRAICEXPRESSIONS

1.Additionofalgebraicexpressionswithexamples




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3.ALGEBRAICEXPRESSIONS

2.Subtractionofalgebraicexpressionswithexamples.


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4.MULTIPLICATIONOFALGEBRAICEXPRESSIONS

1.MultiplyingTwoMonomials.


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4.ALGEBRAICEXPRESSIONSWHICHARENOTPOLYNOMIALS

1.Algebraicexpressionswhicharenotpolynomials





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2.RULE1Thecoefficientoftheproductsoftwomonomialsisequaltotheproductsoftheircoefficients.


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3.RULE2Thevariablepartintheproductsoftwomonomialsisequaltotheproductofthevariablepartsinthegivenmonomials.


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4.Multiplicationofamonomialandabinomial


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5.MULTIPLICATIONOFTWOBINOMIALS

1.(1)ColumnMethod


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5.DIVISIONOFPOLYNOMIALINONEVARIABLE

1.Divisionofapolynomialbyamonomial


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5.MULTIPLICATIONOFTWOBINOMIALS

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


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2.Divisionofapolynomialbyabinomialbyusinglongdivision


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3.Divisionalgorithmforpolynomials



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4.Analternativeandshorterformoflongdivision


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6.IDENTITIES

1.IDENTITY:Anidentityisanequalitywhichistrueforallvaluesofthevariables.


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6.DIVISIONOFPOLYNOMIALBYUSINGFACTORIZATION

1.Divisionofpolynomialbyusingfactorization


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6.IDENTITIES

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



6.IDENTITIES

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


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6.IDENTITIES

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


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6.IDENTITIES

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


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6.IDENTITIES

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

1

x2(ii)x4 +

1

x4



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436.IDENTITIES

7.Ifx -1x= 9findx2 +

1

x2.


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6.IDENTITIES

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


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6.IDENTITIES

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

(iii)(93)2


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6.IDENTITIES

10.Whatmustbeaddedto9x2 - 24x + 10tomakeitawholesquare?



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477.ASPECIALPRODUCT

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


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7.ASPECIALPRODUCT

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


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8.ACTIVITIESFORVERIFYINGTHEIDENTITIES

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


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2.Verificationofidentity(a-b)^2


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

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


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BOARDS CONCEPTS BOOSTER ALGEBRAIC ......4 CONCEPT FOR BOARDS || Chapter ALGEBRAIC EXPRESSIONS AND...

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