Course Content
Class 7th Science
0/36
Class 7th Math
0/71
Class 7 Social Science Geography
0/20
Class 7 Social Science History
0/20
Class 7 Social Science Civics
0/19
Class 7 English Honeycomb
0/20
Class 7 English Honeycomb Poem
0/18
Class 7 English An Alien Hand Supplementary
0/20
Online Class For 7th Standard Students (CBSE)

## Introduction to Algebraic Expressions

### Constant

ConstantĀ is a quantity which has a fixed value.

### Terms of Expression

Parts of an expression which are formed separately first and then added are known asĀ terms. They are added to form expressions.

Example: Terms 4x and 5 are added to form the expression (4x +5).

### Coefficient of a term

The numerical factor of a term is calledĀ coefficientĀ of the term.
Example: 10 is the coefficient of the term 10xy in the expression 10xy+4y.

### Writing Number patterns and rules related to them

• If a natural number is denoted by n, its successor is (n + 1).
Example: Successor of n=10 is n+1 =11.
• If a natural number is denoted by n, 2n is an evenĀ number and (2n+1) an odd number.
Example: If n=10, then 2n = 20 is an even number and 2n+1 = 21 is an odd number.

### Writing Number patterns and rules related to them

• If a natural number is denoted by n, its successor is (n + 1).
Example: Successor of n=10 is n+1 =11.
• If a natural number is denoted by n, 2n is an evenĀ number and (2n+1) an odd number.
Example: If n=10, then 2n = 20 is an even number and 2n+1 = 21 is an odd number.

### Writing Patterns in Geometry

• Algebraic expressions are used in writing patterns followed by geometrical figures.
Example: Number of diagonals we can draw from one vertex of a polygon of n sides is (n ā 3).

## Definition of Variables

• Any algebraic expression can have any number of variables and constants.
• ### Variable

• A variable is aĀ quantity that is prone to change with the context of the situation.
• a,x,p,ā¦ are used to denote variables.
• ### Constant

• It is a quantity which has a fixed value.
• In the expression 5x+4, the variable here is x and the constant is 4.
• The value 5x and 4 are also called terms of expression.
• In the term 5x, 5 is called the coefficient of x. Coefficients are any numerical factor of a term.

### Factors of a term

Factors of a term are quantities which can not be further factorised. A term is a product of its factors.
Example: The term ā3xy is a product of the factors ā3, x and y.

## Formation of Algebraic Expressions

• Variables and numbers are used to construct terms.
• These terms along with a combination of operators constitute an algebraic expression.
• The algebraic expression has a value that depends on the values of the variables.
• For example, let 6p2ā3p+5 be an algebraic expression with variable p
The value of the expression when p=2 is,
6(2)2Ā ā 3(2) + 5
āĀ 6(4) ā 6 + 5 = 23
The value of the expression when p=1 is,
6(1)2Ā ā 3(1) + 5
āĀ 6 ā 3 + 5 = 8

## Like and Unlike Terms

### Like terms

• Terms havingĀ same algebraic factors are like terms.
Example: 8xy and 3xy are like terms.

### Unlike terms

• Terms having different algebraic factors are unlike terms.
Example: 7xy and ā3x are unlike terms.

## Monomial, Binomial, Trinomial and Polynomial Terms

### Types of expressions based on the number of terms

Based on the number of terms present, algebraic expressions are classified as:

• Monomial:Ā An expression with only one term.
Example: 7xy, ā5m,Ā etc.
• Binomial:Ā An expression which contains two, unlikeĀ terms.
Example: 5mn+4, x+y, etc
• Trinomial:Ā An expression which contains three terms.
Example: x+y+5, a+b+ab, etc.

### Polynomials

• An expression with one or more terms.
Example: x+y, 3xy+6+y, etc.

## Addition and Subtraction of Algebraic Equations

• Mathematical operations like addition and subtraction can be applied to algebraic terms.
• For adding or subtracting two or more algebraic expression, like terms of both the expressions are grouped together andĀ unlike terms are retained as it is.
• SumĀ of two or more like termsĀ is a like term with a numerical coefficient equal to the sum of the numerical coefficients of all like terms.
• Difference between two like terms is a like term with a numerical coefficient equal to the difference between the numerical coefficients of the two like terms.
• For example, 2y + 3x ā 2x + 4y
āĀ x(3ā2) + y(2+4)
āĀ x+6y
• Summation of algebraic expressions can be done in two ways:
Consider the summation of the algebraic expressionsĀ 5a2+7a+2ab and 7a2+9a+11b
• Horizontal method
5a2+7a+2ab+7a2+9a+11b
= (5+7)a2+(7+9)a+2ab+11b
= 12a2+16a+2ab+11b
• Vertical method
5a2+7a+2ab
7a2+9a+11b

## Addition and Subtraction of Algebraic Equations

• Mathematical operations like addition and subtraction can be applied to algebraic terms.
• For adding or subtracting two or more algebraic expression, like terms of both the expressions are grouped together andĀ unlike terms are retained as it is.
• SumĀ of two or more like termsĀ is a like term with a numerical coefficient equal to the sum of the numerical coefficients of all like terms.
• Difference between two like terms is a like term with a numerical coefficient equal to the difference between the numerical coefficients of the two like terms.
• For example, 2y + 3x ā 2x + 4y
āĀ x(3ā2) + y(2+4)
āĀ x+6y
• Summation of algebraic expressions can be done in two ways:
Consider the summation of the algebraic expressionsĀ 5a2+7a+2ab and 7a2+9a+11b
• Horizontal method
5a2+7a+2ab+7a2+9a+11b
= (5+7)a2+(7+9)a+2ab+11b
= 12a2+16a+2ab+11b
• Vertical method
5a2+7a+2ab
7a2+9a+11b
ĀÆĀÆĀÆĀÆĀÆĀÆĀÆĀÆĀÆĀÆĀÆĀÆĀÆĀÆĀÆĀÆĀÆĀÆĀÆĀÆĀÆĀÆĀÆĀÆĀÆĀÆĀÆĀÆĀÆĀÆĀÆĀÆĀÆĀÆĀÆĀÆĀÆĀÆĀÆĀÆĀÆĀÆĀÆĀÆĀÆĀÆĀÆĀÆĀÆĀÆĀÆĀÆĀÆĀÆ
12a2+16a+2ab+11b

### Use of algebraic expressions in the formula of the perimeter of figures

Algebraic expressions can be used in formulating perimeter of figures.
Example: Let l be the length of one side then the perimeter of:
Equilateral triangle = 3l
Square = 4l
Regular pentagon = 5l

### Use of algebraic expressions in formula of area of figures

Algebraic expressions can be used in formulation area of figures.
Example: LetĀ lĀ beĀ the length andĀ bĀ be the breadth then the area of:
Square = l2
Rectangle = lĆb = lb
Triangle =Ā bĆh/2, where b and h are base and height, respectively.

Ā

Join the conversation