Topics
Number System(Consolidating the Sense of Numberness)
Number System
Estimation
Ratio and Proportion
Algebra
Numbers in India and International System (With Comparison)
Geometry
Place Value
Mensuration
Natural Numbers and Whole Numbers (Including Patterns)
Data Handling
Negative Numbers and Integers
Number Line
HCF and LCM
Playing with Numbers
- Simplification of Brackets
- Finding Factors Using Rectangular Arrangements and Division
- Factors and Common Factors
- Multiples and Common Multiples
- Concept of Even and Odd Number
- Tests for Divisibility of Numbers
- Divisibility by 2
- Divisibility by 4
- Divisibility by 8
- Divisibility by 3
- Divisibility by 6
- Divisibility by 9
- Divisibility by 5
- Divisibility by 11
Sets
Ratio
Proportion (Including Word Problems)
Unitary Method
Fractions
- Concept of Fraction
- Types of Fractions
- Concept of Proper and Improper Fractions
- Concept of Mixed Fractions
- Like and Unlike Fraction
- Concept of Equivalent Fractions
- Conversion between Improper and Mixed fraction
- Conversion between Unlike and Like Fractions
- Simplest Form of a Fractions
- Comparing Fractions
- Addition of Fraction
- Subtraction of Fraction
- Multiplication of Fraction
- Division of Fractions
- Using Operator 'Of' with Multiplication and Division
- BODMAS Rule
- Problems Based on Fraction
Decimal Fractions
Percent (Percentage)
Idea of Speed, Distance and Time
Fundamental Concepts
Fundamental Operations (Related to Algebraic Expressions)
Substitution (Including Use of Brackets as Grouping Symbols)
Framing Algebraic Expressions (Including Evaluation)
Simple (Linear) Equations (Including Word Problems)
Fundamental Concepts
Angles (With Their Types)
Properties of Angles and Lines (Including Parallel Lines)
Triangles (Including Types, Properties and Constructions)
Quadrilateral
Polygons
The Circle
Symmetry (Including Constructions on Symmetry)
Recognition of Solids
Perimeter and Area of Plane Figures
Data Handling (Including Pictograph and Bar Graph)
Mean and Median
- Introduction
- Row Method
- Column Method
- Example 1
- Example 2
- Example 3
- Key Points Summary
Introduction
A polynomial is an algebraic expression made up of terms that involve variables raised to non-negative integer powers. The addition of polynomials involves combining like terms (terms with the same variable and exponent) from different polynomials. There are two common methods for adding polynomials:
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Row Method
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Column Method
Row Method
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Write the given polynomials in a row.
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Group the like terms together.
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Add the like terms.
Column Method
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Arrange the given polynomials so that like terms are directly under one another in a vertical column.
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Add the terms column-wise.
Example 1
Add 4a + 2b, 3a − 3b + c and −2a + 4b + 2c.
Solution:
= (4a + 2b) + (3a − 3b + c) + (−2a + 4b + 2c) [Step 1]
= 4a + 2b + 3a − 3b + c − 2a + 4b + 2c [Step 2]
= 4a + 3a − 2a + 2b − 3b + 4b + c + 2c [Step 3]
= 5a + 3b + 3c
Example 2
Row Method
Add 3x³ − 5x² + 8x + 10, 15x³ − 6x − 23 and 9x² − 4x + 15.
Solution:
(3x³ − 5x² + 8x + 10) + (15x³ − 6x − 23) + (9x² − 4x + 15)
= 3x³ - 5x² + 8x + 10 + 15x³ − 6x − 23 + 9x² − 4x + 15
= 3x³ + 15x³ − 5x² + 9x² + 8x − 6x − 4x + 10 − 23 + 15
= 18x³ + 4x² + 8x - 10x + 25 − 23
= 18x³ + 4x² − 2x + 2
Example 3
Column Method
Add: 3x³ − 5x² + 8x + 10, 15x³ − 6x − 23 and 9x² − 4x + 15.
3x³ − 5x² + 8x + 10
15x³ − 6x − 23
+ 9x² − 4x + 15
18x³ + 4x² − 2x + 2
Key Points Summary
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Identify like terms by matching variables and exponents.
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Choose a method: row for linear addition, column for clarity.
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Group, then add coefficients only.
