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Algebraic Expressions and Identities Class 8 Notes CBSE Maths Chapter 9 (Free PDF Download)

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Revision Notes for CBSE Class 8 Maths Chapter 9 Algebraic Expressions and Identities - Free PDF Download

For a Class 8 student, it becomes quite difficult for the student to understand the rise in the level of complexity from previous classes. Also, for subjects like Mathematics, it is important for you to be attentive at all times. The subject influences a lot of importance in both your educational and personal life. For a better level of understanding, it is highly important to conquer your basic concepts and formulas of the chapter first and then further move to solve the numerical questions given in the chapter.

Vedantu is a platform that provides free NCERT Solution and other study materials for students. Science Students who are looking for NCERT Solutions for Class 8 Science will also find the Solutions curated by our Master Teachers really Helpful.

You can also download NCERT Solutions Class 8 Maths to help you to revise complete syllabus ans score more marks in your examinations.

Download CBSE Class 8 Maths Revision Notes 2023-24 PDF

Also, check CBSE Class 8 Maths revision notes for All chapters:


Access Class 8 Maths Chapter 9 - Algebraic Expressions and Identities

What are Expressions?

  • Expressions are mathematical sentences which include at least two constant, variables or both connected by mathematical operations.

  • For example: \[3+5,x-y,5+y\] etc.

  • Number line and expression: An expression can be shown on a number line as shown by the example below

  • For example: To show $x+3$ on a number line 

  • Make $x$ at any distance on the number line then move $3$ units right of $x$. The point P shows $x+3$ on a number line 


An expression shown on a number line


  • Similarly, if we have to show $x-4$ on the number line Make $x$ at any distance on the number line then move $4$ units left of $x$.


Terms, Factors and Coefficients

  • Terms are the building blocks of an expression. It may be single number, single variable, product of variables, product of numbers or product of number and variable both.

For example: In expression $3x+5y$ there are two terms $3x$ and $5y$ 

  • Factors are number or algebraic expressions that completely divide another number or expression. 

For example: In expression $5y$ the factors are $5$ and $y$ 

  • The numerical factor of a term is called coefficients

For example: In expression $5x+7y$ , $5$ and $7$ are the coefficients of $x$ and $y$  respectively


Monomials, Binomials, Polynomials

  • Expression that contains only one term is called monomial 

For example: $5y,3x,{{x}^{2}},9,ab$ etc. are monomials 

  • Expression that contains two term is called binomial 

For example: $2x+y,4{{y}^{2}}+z,ab+mn$ etc. are binomials

  • Expression that contains three term is called trinomial 

For example: $x+y+z,2a+b+7c,{{a}^{2}}+6b+{{c}^{2}}$ etc.

  • An expression containing one or more terms with non-zero coefficient and with variables having non negative exponents is called a polynomial.

  • A polynomial may contain any number of terms.

For example: $2x+y,4xy,a+b+c,{{m}^{2}}$ etc. are polynomials


Like and Unlike Terms

  • Like terms are those terms which have the same variable, power of the variable should also be same and coefficient can be different.

For example: $6x$ and $8x$ are the like terms 

  • Unlike terms are opposite of like terms it has different variables.

For example: $5y$ and $9a$ are unlike terms


Addition and Subtraction of Algebraic Expressions

  • In addition, like terms are added.

For example: Add of $3a+5b+2ab$ and $2a+3b+7ab$ 

Write like terms below one another then add 

$3a+5b+2ab $ 

$+2a+3b+7ab $

$ \overline{5a+8b+9ab} $ 

  • In subtraction also only like terms are subtracted.

For example: Subtract ${{x}^{2}}+2x-4xy$ and $3{{x}^{2}}+2xy$ 

Write like terms below one another then subtract 

$ {{x}^{2}}+2x-4xy $ 

$ +3{{x}^{2}}+2xy $

$ \overline{-2{{x}^{2}}+2x-6xy} $ 


Multiplication of Algebraic Expression

1. Multiplying a Monomial by a Monomial

  • The product of two monomial is always a monomial

  • For example: Multiplication of $20xy$ and $4z$  is $20xy\times 4z=80xyz$ 

Multiplication of $7z,2{{x}^{2}}$ and $4y$ is $7z\times 2{{x}^{2}}\times 4y=56{{x}^{2}}yz$ 


2. Multiplying a Monomial by a Polynomial

  • Use distributive law to multiply a monomial by a polynomial i.e., multiply monomial to each term of polynomial

  • For example: Multiplication of $6x$ and $3{{x}^{2}}+5y$ is 

$\left( 6x \right)\times \left( 3{{x}^{2}}+5y \right)=\left( 6x\times 3{{x}^{2}} \right)+\left( 6x\times 5y \right)$ 

$=18{{x}^{3}}+30xy$ 


3. Multiplying a Polynomial by a Polynomial

  • Multiply each term of a polynomial by each term of another polynomial then combine like terms if any

  • For example: Multiplication of $\left( 2x+3y \right)$ and $\left( 2x-3y+z \right)$ is

$\left( 2x+3y \right)\times \left( 2x-3y+z \right)=\left( 2x \right)\left( 2x-3y+z \right)+\left( 3y \right)\left( 2x-3y+z \right)$ 

$=\left( \left( 2x \right)\left( 2x \right)-\left( 2x \right)\left( 3y \right)+\left( 2x \right)\left( z \right) \right)+\left( \left( 3y \right)\left( 2x \right)-\left( 3y \right)\left( 3y \right)+\left( 3y \right)\left( z \right) \right)$ 

$=\left( 4{{x}^{2}}-6xy+2xz \right)+\left( 6xy-9{{y}^{2}}+3yz \right)$ 

$=4{{x}^{2}}+2xz-9{{y}^{2}}+3yz$ 


Identity

  • An equation is not true for any value of variable but for certain values.

  • The equation which is always true for any value of variables is called identity.


  • Standard Identities

The following identities are known as standard identities

  1. ${{\left( a+b \right)}^{2}}={{a}^{2}}+{{b}^{2}}+2ab$ 

  2. ${{\left( a-b \right)}^{2}}={{a}^{2}}+{{b}^{2}}-2ab$ 

  3. $\left( a+b \right)\left( a-b \right)={{a}^{2}}-{{b}^{2}}$ 


  • Another Useful Identity

$\left( x+a \right)\left( x+b \right)={{x}^{2}}+\left( a+b \right)x+ab$ 

  • These identities make calculation easier.


Download Revision Notes Class 8 Maths Chapter 9 - Free PDF

Class 8 students preparing for Chapter 9 Algebraic Expressions and Identities may wonder where to find the exact Algebraic Expressions and Identities Class 8 Notes for a better understanding of the chapter. This is the reason why Vedantu is bringing Algebraic Expressions and Identities Class 8 Note right in front of you. These revision notes include all the important topics and formulas of the chapter in one single page so that you don't face any problem.

Revision Notes Class 8 Maths Chapter 9 proves to be tremendously important for the students eager to complete the entire chapter in less time. These revision notes are prepared by subject matter experts at Vedantu who have extensive years of experience in teaching Mathematics. Algebraic Expressions and Identities Class 8 Notes will improve your knowledge and will be useful in understanding the important concepts of the chapter before the examination.

Download Revision Notes Class 8 Maths for better preparation of Chapter. These revision notes are designed as per the latest NCERT syllabus issued by the CBSE board. Students of class 8 can download free Class 8 Maths Chapter 9 Revision Notes just with a single click on the PDF link given on this page.


A Few Glimpses of Chapter 9 Algebraic Expressions and Identities

With the previous basic knowledge of algebraic expression or simple expressions such as 9y, 5p - 4q, 3p² -q,  etc, Class 8 Chapter 9 Algebraic Expressions and Identities will help you to explore the world of Algebraic Expression.


Algebraic Expressions

An algebraic expression is an expression that is formed using variables and constants. The expression 9y - 5 is formed using variable y and constant 9 and 5. We know that the value of y in expression 9y - 5 can be anything. It can be either 9, 5, 0, 9/5. etc. There can be unlimited different values. It is important to note that the value of expression varies with the value chosen for the variables it includes. Hence, the value of 9y - 5 goes on changing as y takes different values. For example, when y = 2, 9(2) - 5 = 18 - 5 = 13, when y = 0 , 9(0) - 5 = - 5 etc.


Algebraic Identities

In Mathematics, algebraic identity is an equality that holds despite the value chosen for its variables. Generally, Algebraic identities are used to simplify or rearrange algebraic expression. Through definition, we can state that two sides of identities are replaceable., so we can easily replace one with the other at any time. For example, the identity ( p + q)² = p² + q² + 2pq is true for all the choices of p and q, whether they are complex or real numbers.

Chapter 9 Algebraic Expressions and Identities includes seven exercises and 9 different topics and the Class 8 Maths Revision Notes Chapter 9 PDF provided by Vedantu includes the short and brief explanation of every topic given in the chapter. Now, let us look at the topics discussed in this chapter.

  • What are Expressions

  • Terms, Factors, Coefficients

  • Monomials, Binomials, Polynomials

  • Addition and Subtraction of Algebraic Expressions

  • Like and Unlike Terms

  • Multiplication of  Algebraic Expressions

  • Multiplication of two Monomials

  • Multiplication of three or more Monomials

  • Multiplication of Monomials by Binomials

  • Multiplication of Monomials by Trinomials

  • Multiplication of Polynomial by Polynomial

  • Multiplication of Binomial by Binomial

  • Multiplication of Binomial by Trinomial

  • What is Identity?

  • Standard Identities

  • Applying Identities

Download Class 8 Maths Revision Notes Chapter 9 now and gets the brief explanations of all the topics discussed above.


Key Benefits of Class 8 Maths Revision Notes Chapter 9

Some of the key benefits of Class 8 Maths revision notes Chapter 9 are discussed below:

  • Class 8 Maths Revision Notes Chapter 9 is written in a simple language. Explanations of the topics are to the point. This will help students to go through the important concepts of the chapter with much ease and save time.

  • With Vedantu’s Class 8 revision notes Maths Ch 9, you don't need to wait for someone else to make you understand the concepts or important topics of the chapter. If you refer to these notes, you will be able to understand all the topics by yourself. Simple language and simple explanation of the topics will make your learning process easy.

  • The explanations of the concepts are not written in boring and big paragraphs. All the different topics of the chapter are explained with the help of examples. The example help will surely help in better understanding of the chapter. You can easily remember the concepts with the help of examples that are provided by Vedantu.

  • Class 8 revision notes Maths Ch 9 provides all the concepts and the topics of the chapter right in front of you. It will not let you miss any topic that is of the greatest importance for your examination. Once you revise these notes, you can be sure of one thing that you will be easily able to solve Algebraic Expressions and Identities numerical questions asked in the examination.

  • You can download Class 8 Maths revision notes Chapter 9 Pdf for free. You can download these revision notes on your PC, laptops as well your mobile phone as per your needs.


Conclusion 

The Algebraic Expressions and Identities Class 8 Notes by Vedantu help students understand mathematical concepts in an easy way. This resource, available for free download, covers Chapter 9 of CBSE Maths. The importance of this topic lies in mastering algebraic expressions and identities, which are fundamental in mathematics. These notes break down complex ideas, making them accessible for Class 8 students. With a focus on key concepts, this material aids in building a strong foundation for solving mathematical problems. The free PDF download is a valuable tool for students to enhance their understanding of algebraic expressions and identities.

FAQs on Algebraic Expressions and Identities Class 8 Notes CBSE Maths Chapter 9 (Free PDF Download)

1. What are algebraic expressions and identities?


Algebraic expressions: expressions that are formed using integer constants, variables, and algebraic operations.

Example: 9x3 – 3x2+6xy – z

Algebraic Identities:  it is referred to as equality or an expression that always holds true for every value of variables in them.

Example:  (a + b)3 = a3 + b3 + 3ab (a + b)

You can find detailed explanations of these terms on Vedantu's Notes for Class 8 Mathematics Chapter 9 "Algebraic Expressions and Identities."

2. How should I use Vedantu’s notes to study Chapter 9 of Class 8 Mathematics?

Class 8 Mathematics Chapter 9 "Algebraic Expressions and Identities'' introduces the students to several new terms and concepts. Students must understand these concepts and memorize the terms to help them in mastering this chapter. You can use Vedantu's Revision Notes for "Algebraic Expressions and Identities'' to go over all the important concepts of the chapter in one place. You can also use these notes for a quick revision before every study session and also before exams.

3. Are Vedantu’s revision notes for Chapter 9 of Class 8 Mathematics reliable?

Yes, the notes provided by Vedantu are 100% reliable. The notes are carefully prepared by expert Mathematics teachers.  These experienced teachers prepare the revision notes intending to provide the students with short but comprehensive notes to help them in their studies. Particular attention is given to the fact that every important piece of information from the chapter is mentioned in our revision notes. Our teachers also add simplified explanations of their own to aid in students' understanding of the concepts. 

4. Is Chapter 9 of Class 8 Mathematics difficult?

Chapter 9 of Class 8 Mathematics may appear difficult to some students initially. The reason for this is that there are many new terms and concepts that students may find complicated. However, the fact of the matter is that the chapter is extremely intriguing and once you get the hang of the concepts you will enjoy solving all 5 exercises. Make efforts to understand the chapter and then treat every question like an interesting puzzle and you find this chapter a piece of cake. 

5. How can I memorize the new terms taught in Chapter 9 of Class 8 Mathematics?

Chapter 9 of Class 8 Mathematics contains many terms to understand and memorize. These include expression, identities, terms, variables, constants, like and unlike terms, monomials, binomials, trinomials, and polynomials. You will also be introduced to some standard algebraic identities that you must memorize as you will be using these identities in upcoming grades as well. Go over every term and identity and daily to memorize them. Write the identities in a separate notebook and go over them. Refer to Vedantu's revision notes for daily revision.