Competitive Exams

IIT JEE, NEET, ESE, GATE, AE/JE, Olympiad

Only IAS

UPSC, State PSC

School Preparation

Foundation (Class 6-12), Commerce, Arts, CuriousJr (1st - 8th), Science, International Boards

Govt Exam

Judiciary, SSC, Defence, Teaching, JAIIB & CAIIB, BIHAR EXAMS WALLAH, UP Exams, Railway, Nursing Exams, Banking, WB Exams

UG & PG Entrance Exams

MBA, IPMAT, IIT JAM, LAW, CUET UG, UGC NET, GMAT, Design & Architecture, Pharma, CSIR NET, CUET PG, NEET PG

FINANCE

CA, CS, Finance Courses, ACCA

Others

Online Degrees

English Proficiency Test

IELTS, TOEFL

Agriculture

CBSE Class 8 Maths Notes Chapter 8 Algebraic Expressions and Identities

Here we have provided CBSE Class 8 Maths Notes Chapter 8 Algebraic Expressions and Identities for the ease of students so that they can prepare better for their exams.

Ananya Gupta23 Aug, 2024

CBSE Class 8 Maths Notes Chapter 8: CBSE Class 8 Maths Chapter 8 Algebraic Expressions and Identities focuses on helping students understand the formation and manipulation of algebraic expressions, including monomials, binomials, and polynomials.

These notes provide a detailed overview of the concepts, ensuring that students can apply these identities in problem-solving and build a strong foundation in algebra.

CBSE Class 8 Maths Notes Chapter 7 Algebraic Expressions and Identities Overview

These notes on CBSE Class 8 Maths Chapter 8 Algebraic Expressions and Identities are prepared by the subject experts of Physics Wallah. They cover important concepts like how to form algebraic expressions and use key identities. The notes are written in a simple way to help students understand the topics easily and build a strong base in algebra. With clear explanations and examples these notes are a great resource for learning the chapter.

CBSE Class 8 Maths Notes Chapter 8 Algebraic PDF Download

The PDF link for CBSE Class 8 Maths Notes Chapter 8 Algebraic Expressions and Identities is available below. It is a valuable resource for students providing clear examples and step-by-step solutions to help them grasp the concepts effectively. Access the PDF to enhance your understanding and practice of algebraic expressions and identities.

CBSE Class 8 Maths Notes Chapter 8 Algebraic Expressions and Identities PDF

CBSE Class 8 Maths Notes Chapter 8 Algebraic Expressions and Identities

Here are the notes for CBSE Class 8 Maths Chapter 8 Algebraic Expressions and Identities. Algebraic expressions are combinations of variables, constants, and mathematical operators without an equal sign, unlike equations. These expressions are made up of terms, which are the building blocks. A term can be a constant, a variable, or a product of both. The factors of a term are the variables or constants that multiply to form that term, and the coefficient is the numerical factor in a term. Algebraic expressions can be classified into monomials (one term), binomials (two terms), and polynomials (more than two terms). When adding or subtracting algebraic expressions, only like terms—those with the same variables and powers can be combined. Multiplication of expressions involves using the distributive property, which helps in expanding and simplifying expressions. These concepts are fundamental for solving algebraic problems and understanding the structure of algebraic expressions.

Algebraic Expressions

Algebraic expressions are mathematical phrases that consist of variables, constants, and operators, but they do not include an equal sign or sides like algebraic equations. These expressions represent a value or relationship between variables and constants.

Examples of algebraic expressions are : $2 x + 4$ , $7 y - 3 + 6 x$ , $3 t^{2} + 4 t - 1$ .

Factors

Factors are the individual variables or constants that, when multiplied together, form a term in an algebraic expression. For example, in the term

, the factors are

p

, and

q

. Each factor contributes to the overall product that makes up the term. Factors are considered to be in their simplest form and cannot be broken down or factorized further. They are essential building blocks in constructing algebraic expressions, and understanding them helps in simplifying and manipulating these expressions.

Coefficients

The coefficient of a term is the numerical factor that multiplies the variables within that term. It indicates how many times the variables are being multiplied. For instance, in the term

, the coefficient is

, and in the term

, the coefficient is

. Coefficients are crucial in algebra as they determine the weight or magnitude of the variables they are associated with. They play a significant role in simplifying expressions and solving equations.

Like Terms

Like terms are terms in an algebraic expression that share the same variables raised to the same power. These terms have identical algebraic factors, though their numerical coefficients may differ. For example,

3 x^{2} y

and

5 x^{2} y

are like terms.

Monomial

A monomial is an algebraic expression consisting of only one term. It can include constants, variables, or both, but it remains a single, indivisible unit. The term can be a product of numbers and variables, and it is not separated by plus or minus signs. Examples of monomials include:

: A product of the constant 6 and the variable
: A product of the constant 7 and the variables and .
: A product of the constant 9 and the variables , , and
: A product of the constant 4 and the variables and .

Binomial

A binomial is an algebraic expression that contains exactly two unlike terms separated by a plus (+) or minus (−) sign. Each term in a binomial can be a constant, a variable, or a product of variables, but the crucial aspect is that there are only two distinct terms. Examples of binomials include:

: This binomial consists of two terms, and , connected by a minus sign.
This expression has two terms, , connected by a minus sign.
: This binomial includes the terms and , joined by a plus sign.

Polynomial

A polynomial is an algebraic expression that consists of more than two terms, where each term has a non-zero coefficient and variables with non-negative integer exponents. Polynomials are defined by their terms, which can include constants, variables, and products of variables. The key characteristics of polynomials are that they do not have division by variables and the exponents of the variables are non-negative integers. Examples of polynomials include:

Examples:

a + b + c + 2, 7 x y - 8 x + 2 + 3 y, 5 t^{3} - 7 t + k + 3.

Algebraic Identities

$(a + b)^{2} = a^{2} + 2 a b + b^{2}$
$(a - b)^{2} = a^{2} - 2 a b + b^{2}$
$(a + b) (a - b) = a^{2} - b^{2}$

Addition and Subtraction of Algebraic Expressions

When adding or subtracting algebraic expressions, it is essential to combine like terms. Like terms are terms that have the same variables raised to the same powers, but may have different numerical coefficients. To add or subtract algebraic expressions:

Identify Like Terms : Group terms that have identical variable parts.
Add or Subtract Coefficients : Combine the numerical coefficients of the like terms.

(3 x^{2} y + 4 x^{2} y) + (y) + (7 a) + (z + 5 z) = 7 x^{2} y + y + 7 a + 6 z

Multiplication of Algebraic Expressions

Multiplication of Monomials

When multiplying two monomials, follow these steps:

Multiply Numerical Coefficients : Multiply the numerical coefficients of the monomials to find the new numerical coefficient of the product.

Combine Like Variables : For each variable, add the exponents from both monomials. This results in the new exponent for that variable in the product.

Multiplying two monomials:

$x \times 3 y = x \times 3 \times y = 3 \times x \times y = 3 x y$
$3 x \times 2 y = 3 \times x \times 2 \times y = 3 \times 2 \times x \times y = 6 x y$
$5 x \times (- 2 z) = 5 \times (- 2) \times x \times z = - 10 x z$

Multiplying three or more monomials:

$2 x \times 3 y \times 5 z = (2 x \times 3 y) \times 5 z = 6 x y \times 5 z = 30 x y z$
$4 x y \times 5 x^{2} y^{2} \times 6 x^{3} y^{3} = (4 x y \times 5 x^{2} y^{2}) \times 6 x^{3} y^{3} = 20 x^{3} y^{3} \times 6 x^{3} y^{3} = 120 x^{6} y^{6}$

Distributive Property of Multiplication

The distributive property of multiplication states that when you multiply a number by a sum or difference, you can distribute the multiplication across each term within the parentheses. This property simplifies algebraic expressions and calculations. Consider the expression :

6 \times (2 + 4 x)

= (6 \times 2) + (6 \times 4 x)

= 12 + 24 x

Multiplication of Polynomials

When multiplying two polynomials, each term in the first polynomial is multiplied by every term in the second polynomial. This process is known as the distributive property and ensures that every term from one polynomial interacts with every term from the other polynomial.

Steps for Multiplying Polynomials:

Distribute Each Term: Multiply each term in the first polynomial by each term in the second polynomial.

Combine Like Terms: After performing the multiplications, combine all the like terms to simplify the resulting polynomial.

Multiplying a binomial by a binomial

(3a + 4b) × (2a + 3b) = 3a × (2a + 3b) + 4b × (2a + 3b) = (3a × 2a) + (3a × 3b) + (4b × 2a) + (4b × 3b) = 6a ² + 9ab + 8ab + 12b ² = 6a ² + 17ab + 12b ² When we multiply a binomial by a trinomial, each of the three terms of the trinomial is multiplied by each of the two terms of the binomial.

Multiplying a binomial by a trinomial

(p + 4) × (p ² + 2p + 3) = p × (p ² + 2p + 3) + 4 × (p ² + 2p + 3) = (p ³ + 2p ² + 3p) + (4p ² + 8p + 12) = p ³ + 6p ² + 11p + 12

Benefits of CBSE Class 8 Maths Notes Chapter 8 Algebraic Expressions and Identities

Clear Understanding: The notes provide a clear and structured explanation of algebraic expressions and identities making complex concepts more accessible and easier to understand for Class 8 students.
Comprehensive Coverage: They cover all essential aspects of algebraic expressions, including terms, factors, coefficients, and types of polynomials. This thorough coverage ensures that students grasp the full scope of the topic.
Simplified Explanations: Concepts such as addition, subtraction and multiplication of algebraic expressions are explained in simple terms, aiding in better comprehension and retention of the material.
Improved Problem-Solving Skills: By working through various problems and examples, students develop strong problem-solving skills and become proficient in handling different types of algebraic expressions and identities.
Enhanced Preparation: The notes are designed to align with the CBSE curriculum ensuring that students are well-prepared for exams and assessments. They help in reinforcing classroom learning and boosting exam performance.

CBSE Class 8 Maths Notes Chapter 8 FAQs

What is an algebraic expression?

An algebraic expression is a mathematical phrase that includes variables, constants, and operators (such as +, −, ×, ÷). It does not contain an equal sign.

What are terms in an algebraic expression?

Terms are the individual parts of an algebraic expression separated by addition or subtraction signs.

What is a coefficient?

A coefficient is the numerical factor multiplied by a variable in a term. For instance, in the term 7x, 7 is the coefficient.

What are like terms?

Like terms are terms that have the same variables raised to the same power. They can be combined through addition or subtraction.

How do you add or subtract algebraic expressions?

To add or subtract algebraic expressions, combine like terms by adding or subtracting their coefficients.

🔥 Trending Blogs

CBSE Important Questions for Class 8 Subject Wise

CBSE Class 8 Hindi Syllabus 2025-26, Check Updated Syllabus

CBSE Class 8 Syllabus 2025-26, Download Subject Wise Syllabus PDF

CBSE Class 8 Maths Syllabus 2025-26, Check Updated Syllabus

CBSE Class 8 Social Science Syllabus 2025-26, Latest PDF Download

Talk to a counsellorHave doubts? Our support team will be happy to assist you!

08448982616

008448982616

Check out these Related Articles

CLASS 8 EXAM

CBSE Class 6 Hindi Syllabus 2025-26, Unit Wise Syllabus

Read Full Story

12 May 2025, 05:47 pm

CLASS 8 EXAM

CBSE Class 8 Science Syllabus 2025-26, Check Updated Syllabus

Read Full Story

8 May 2025, 11:29 am

CLASS 8 EXAM

CBSE Class 8 English Syllabus 2025-26, Chapter Wise Syllabus

Read Full Story

12 May 2025, 07:16 pm

CLASS 8 EXAM

CBSE Class 8 English It So Happened Chapter 8 Notes

Read Full Story

30 Apr 2025, 12:32 pm

CLASS 8 EXAM

CBSE Class 8 English Honeydew Chapter 3 Notes

Read Full Story

30 Apr 2025, 03:32 pm

CLASS 8 EXAM

CBSE Class 8 English Chapter Wise Notes List Here

Read Full Story

29 Apr 2025, 12:01 pm

CLASS 8 EXAM

CBSE Class 8 English Honeydew Notes Chapter Wise Notes Summary

Read Full Story

29 Apr 2025, 11:55 am

CLASS 8 EXAM

CBSE Class 8 English It So Happened Notes Chapter Wise PDF

Read Full Story

28 Apr 2025, 04:31 pm

CLASS 8 EXAM

CBSE Class 8 English It So Happened Chapter 4 The Treasure Within Notes

Read Full Story

26 Apr 2025, 12:11 pm

Join 15 Million students on the app today!

Live & recorded classes available at ease

Dashboard for progress tracking

Millions of practice questions at your fingertips

Free Learning Resources

PW Books

Notes (Class 10-12)

Class 10 Math's Notes

Class 10 Chemistry Notes

Class 10 Physics Notes

Class 10 Biology Notes

Aptitude & Reasoning

Class 10 Geography

Physics Class 11 Notes

Class 11 Chemistry Notes

Maths Notes Class 11

Zoology Class 11

Class 11 Botany Notes

Physics Class 12 notes

Chemistry Class 12

Maths Notes Class 12

Zoology class 12

Class 12th Botany Notes

PW Study Materials

Arjuna JEE Study Material

JEE 7 PYQs

JEE Mind Maps

Yakeen Study Material

NCERT Punch

Arjuna Neet Study Material

NEET PYQs

CBSE Sample Paper

CBSE Question Bank

Udaan For Class 10th Study Material

Notes (Class 6-9)

Class-6 Theory & Notes

Math's Notes for class 7

Science Notes for class 7

Class 8 Math Notes

Class 8 Chemistry Notes

Class 8 Physics Notes

Class 8 Biology Notes

Class 8 SST Notes

Class 9 Math's Notes

Class 9 Physics Notes

Class 9 Chemistry Notes

Class 9 Biology Notes

Ncert Solutions

NCERT Solutions For Class 6

NCERT Solutions For class 7

NCERT Solutions for class 8

NCERT Solutions for class 9

NCERT Solutions for class 10

NCERT Solutions for class 11

NCERT Solutions for Class 12

Govt Exams

Entrance Exams

Our Other Websites

Class 6th to 12th Online Courses

Class 12 Online Course

Class 11 Online Course

Class 10 Online Course

Class 9 Online Course

Class 8 Online Course

Govt Job Exams Courses

SSC Online Coaching

Bank Exam Online Coaching

TET Online Coaching

JAIIB & CAIIB Online Coaching

Bihar Exam Online Coaching

UPSC Coaching

UPSC Online Coaching

UPSC Offline & Hybrid Coaching

State PSC Online Coaching

UPPSC Online Coaching

BPSC Online Coaching

Defence Exam Coaching

NDA Online Coaching

CDS Online Coaching

AFCAT Online Coaching

Agniveer Online Coaching

Gate Exam Coaching

Civil Engineering Courses

Mechanical Engineering Courses

Formulas

Other Exams

Company Secretary Exam

Know about Physics Wallah

Physics Wallah is an Indian edtech platform that provides accessible & comprehensive learning experiences to students from Class 6th to postgraduate level. We also provide extensive NCERT solutions, sample paper, NEET, JEE Mains, BITSAT previous year papers & more such resources to students. Physics Wallah also caters to over 3.5 million registered students and over 78 lakh+ Youtube subscribers with 4.8 rating on its app.

We Stand Out because

We provide students with intensive courses with India’s qualified & experienced faculties & mentors. PW strives to make the learning experience comprehensive and accessible for students of all sections of society. We believe in empowering every single student who couldn't dream of a good career in engineering and medical field earlier.

Our Key Focus Areas

Physics Wallah's main focus is to make the learning experience as economical as possible for all students. With our affordable courses like Lakshya, Udaan and Arjuna and many others, we have been able to provide a platform for lakhs of aspirants. From providing Chemistry, Maths, Physics formula to giving e-books of eminent authors like RD Sharma, RS Aggarwal and Lakhmir Singh, PW focuses on every single student's need for preparation.

What Makes Us Different

Physics Wallah strives to develop a comprehensive pedagogical structure for students, where they get a state-of-the-art learning experience with study material and resources. Apart from catering students preparing for JEE Mains and NEET, PW also provides study material for each state board like Uttar Pradesh, Bihar, and others