CBSE Class 8 Maths Revision Notes Chapter 9

 CBSE Class 8 Mathematics Revision Notes Chapter 9 – Algebraic Expressions and Identities

Class 8 Mathematics, Chapter 9 notes, Algebraic Expressions and Identities have been provided by subject experts at Extramarks. Class 8 Chapter 9 Mathematics notes will help students prepare for the exam and grasp every concept. 

Our expert faculties also provide important questions based on CBSE question papers and all the critical formulas written in one place based on NCERT books.

Revision Notes for CBSE Class 8 Mathematics Chapter 9 – Free PDF Download

Access Class 8 Mathematics Chapter 9 – Algebraic Expressions and Identities

What are Expressions?

• The mathematical statements connected by mathematical operations that include two variables, constants, or both are expressions.
• Examples are: 2+8, a-b, 4+b etc. 
• Expression and Number Line: An expression can be represented on a number line, as shown below.
• For example: To show a+2 on a number line.
• Mark x at any distance on the number line and move 2 units right of x. Point y shows a+2 on a number line. 
• Likewise, we can also show a-2 on a number line. We mark x at any distance on a number line and move 2 units left to x. 

Terms, Factors, and Coefficients

• The individual building blocks of an equation are terms; they might be a whole number or a product of numbers, a single variable or a product of different variables, or a product of numbers and variables. So, for example, 2a+2b, there are two terms in this expression, 2a and 2b.Factors form the terms of an equation. For example, 6xy is the term, and 6, x, and y form factors for this term. Factors are numbers that are divided entirely into other numbers or expressions.
• Coefficients are the numerical factors of the term. For example, 4x+7y, 4, and 7 are the coefficients of x and y in the given expression.

Monomials, Binomials, Polynomials

• An expression that consists of only one term is called a monomial.

             For example, 2a, 5b, a2, 7, xy, etc., are all monomials.

• An expression that consists of two terms is called a binomial.

             For example: 2a+b, 2a2+b, xy+pq etc. are all binomials.

• An expression that consists of three terms is called a trinomial.

             For example: a+b+c, 2x+3y+8z, a2+3b+6c etc.

• An expression that contains one or more terms with non-zero coefficients and variables having non-negative exponents is called a polynomial. A Polynomial can consist of any number of terms.

             For example: 2a+b, 3ab, x+y+z,c2etc.

Like and Unlike Terms

• Terms having the same variables are called like terms; the power of the variables must be the same, and the coefficient can be different. For example, 6a and 2a are like terms.
• Unlike terms that have different variables, they are the opposite of like terms. For example, 7b and 3a are unlike terms.

Addition and Subtraction of Algebraic Expressions

• Terms are added in addition and subtracted in subtraction.
•  For example, the addition of 3x+5y+2xy and 2x+3y+7xy is given below.

                        3x + 5y + 2xy

                     + 2x + 3y + 7xy

                        5x + 8y + 9xy

• For example, subtraction of a2+2a-4ab and 3×2+2xy is given below

                        a2+ 2a – 4ab

                   – 3a2          + 2ab

                     -2a2 +2a – 6ab

Multiplication of Algebraic Expressions

1. Multiplication of two Monomials:

When two monomials are multiplied, the product is always a monomial.

For example: multiplication of 20ab and 4c is 20ab X 4c = 80abc

Product of 7a, 2b2 and 4y is 7z X 2x2 X 4y = 56x2yz

2. Multiplying a Monomial by a Polynomial:

Distributive laws are applied to multiply a polynomial by any monomial, where each polynomial term is multiplied by the monomial.

For example multiplication of 6a and 3a2 +5b is

 (6a) X (3a2+5b)= (6a X 3a2) + (6a X 5y) = 18a3 + 30ab

3. Multiplication of two Polynomials:

Multiplication of two polynomials gives a polynomial. 

For example : multiplication of (2p+3q) and (2p-3q+y) is

(2p+3q) X (2p-3q+y) = (2p) (2p-3q+y) + (3q) (2p-3q+y)

                                    = ((2p) (2p) – (2p)(3q) + (2p)(y)) + ((3q)(2p) – (3q)(3q) + (3q)(y))

                                    = (4p2 – 6pq + 2py) + (6pq-9q2+3py)

                                    = 4p2+2py-9q2+3qy

Identity

• Identities are equations that are not true for any value of variables but definite values. 
• Equations always valid for any value of variables are called an identity.
• Standard Identities: Following are the standard identities.

              (a+b)2= a2 + b2+ 2ab

              (a-b)2 =a2 + b2– 2ab

              (a+b) (a-b) = a2 – b2

• Another useful Identity to ease the calculations.

              (x+a) (x+b) = x2 + (a+b)x + ab

Download Revision Notes Class 8 Mathematics Chapter 9 – Free PDF

Class 8 Mathematics Chapter 9 notes free pdf is a part of CBSE revision notes for a glance of the chapter. Here everything is given according to the NCERT book and as per CBSE guidelines.

A Few Glimpses of Chapter 9 Algebraic Expressions and Identities

• Algebraic expressions are formed of constants, variables, and mathematical operators.
• The term is a product of its factors, which add up to form an expression.
• The product of factors forms the term of an expression.
• The coefficient is the numerical factor of a term.
• Monomials are expressions containing one term; binomials contain two terms; trinomials are expressions containing three terms.
• Multiplication of two monomials gives a monomial. 
• During the multiplication of a polynomial by a monomial, every term in the polynomial is multiplied by the monomial.
• In the multiplication of polynomials by a binomial or trinomial, we multiply term by term of a polynomial into terms of a binomial or trinomial.
• An identity is an equation valid for certain variables’ values only.

Algebraic Expressions

We add or subtract their terms during the addition and subtraction of algebraic expressions. Therefore, the sum and difference of two like terms is a like term. This is because the numerical coefficient of like terms equals the sum of all the terms’ numerical terms. Therefore, the difference between the numerical coefficients of two like terms is a good term. 

Multiplication of Algebraic Expressions

Multiplying two monomials:

The numerical coefficient of a term is equal to the numerical coefficient of both terms. The exponent of each algebraic factor is equal to the sum of the exponents of that algebraic factor of both the monomials.

Example: 

• multiplying two monomials: Xx3y = Xx3xy = 3xXxy = 3xy
• multiplying three or more monomials: 2x X 3y X 5z = (2Xx3y) X 5z = 6xy X 5z = 30xyz

Distributive Property of Multiplication:

The distributive property helps in solving the mathematical expression. It is an algebraic property that can be used to multiply a single value and two or more values within a set of parentheses in the form of a(b+c). 

Let us understand with an expression 6 X (2+4x)

= (6X2) + (6X4x)

= 12 + 24x

Distributive law is to be used to multiply a monomial and a binomial. 

Multiplication of any Polynomial:

Multiplication of two polynomials involves multiplication of all the monomials of one polynomial with all the terms of monomials of another polynomial. 

• Multiplication of two binomials

(3x+ 4y) X (2x + 3y)

=3x X (2x + 3y) + 4y X (2x+3y)

=(3x X 2x) + (3x X 3y) + (4y X 2x) + (4y X 3y)

=6x2 + 9xy + 8xy + 12y2

= 6x2 + 17xy + 12y2

• Multiplication of a binomial by a trinomial
• (p+4) X (p2+2p+3)

             = p X (p2+2p+3) +4 X (p2+2p +3)

             =(p3 +2p2+3p) + (4p2+8p+12)

             = p3+ 6p2+11p+12

Algebraic Identities

   (a+b)2= a2 + b2+ 2ab

   (a-b)2 =a2 + b2– 2ab

   (a+b) (a-b) = a2 – b2

Key Benefits of Class 8 Mathematics Revision Notes Chapter 9

Extramarks experienced faculty prepare chapter 9 math class 8 notes to help students understand the important questions and formulas and get a better grasp of the chapter. These CBSE revision notes will enable students to practise efficiently for the exams and gain a better knowledge of the CBSE syllabus as per NCERT books. Extramarks also provides CBSE extra questions for better exam preparation.