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 ā3xy is a product of the factors ā3, 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 6p^{2}ā3p+5 be an algebraic expression with variable p
The value of the expression when p=2 is,
6(2)^{2Ā }ā 3(2) + 5
āĀ 6(4) ā 6 + 5 = 23
The value of the expression when p=1 is,
6(1)^{2Ā }ā 3(1) + 5
āĀ 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 ā3x 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, ā5m,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
āĀ x(3ā2) + y(2+4)
āĀ x+6y  Summation of algebraic expressions can be done in two ways:
Consider the summation of the algebraic expressionsĀ 5a^{2}+7a+2ab and 7a^{2}+9a+11b  Horizontal method
5a^{2}+7a+2ab+7a^{2}+9a+11b
= (5+7)a^{2}+(7+9)a+2ab+11b
= 12a^{2}+16a+2ab+11b  Vertical method
5a^{2}+7a+2ab
7a^{2}+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
āĀ x(3ā2) + y(2+4)
āĀ x+6y  Summation of algebraic expressions can be done in two ways:
Consider the summation of the algebraic expressionsĀ 5a^{2}+7a+2ab and 7a^{2}+9a+11b  Horizontal method
5a^{2}+7a+2ab+7a^{2}+9a+11b
= (5+7)a^{2}+(7+9)a+2ab+11b
= 12a^{2}+16a+2ab+11b  Vertical method
5a^{2}+7a+2ab
7a^{2}+9a+11b
ĀÆĀÆĀÆĀÆĀÆĀÆĀÆĀÆĀÆĀÆĀÆĀÆĀÆĀÆĀÆĀÆĀÆĀÆĀÆĀÆĀÆĀÆĀÆĀÆĀÆĀÆĀÆĀÆĀÆĀÆĀÆĀÆĀÆĀÆĀÆĀÆĀÆĀÆĀÆĀÆĀÆĀÆĀÆĀÆĀÆĀÆĀÆĀÆĀÆĀÆĀÆĀÆĀÆĀÆ
12a^{2}+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 = l^{2}
Rectangle = lĆb = lb
Triangle =Ā bĆh/2, where b and h are base and height, respectively.
Ā