• NCERT Solutions
    • NCERT Library
  • RD Sharma
    • RD Sharma Class 12 Solutions
    • RD Sharma Class 11 Solutions Free PDF Download
    • RD Sharma Class 10 Solutions
    • RD Sharma Class 9 Solutions
    • RD Sharma Class 8 Solutions
    • RD Sharma Class 7 Solutions
    • RD Sharma Class 6 Solutions
  • Class 12
    • Class 12 Science
      • NCERT Solutions for Class 12 Maths
      • NCERT Solutions for Class 12 Physics
      • NCERT Solutions for Class 12 Chemistry
      • NCERT Solutions for Class 12 Biology
      • NCERT Solutions for Class 12 Economics
      • NCERT Solutions for Class 12 Computer Science (Python)
      • NCERT Solutions for Class 12 Computer Science (C++)
      • NCERT Solutions for Class 12 English
      • NCERT Solutions for Class 12 Hindi
    • Class 12 Commerce
      • NCERT Solutions for Class 12 Maths
      • NCERT Solutions for Class 12 Business Studies
      • NCERT Solutions for Class 12 Accountancy
      • NCERT Solutions for Class 12 Micro Economics
      • NCERT Solutions for Class 12 Macro Economics
      • NCERT Solutions for Class 12 Entrepreneurship
    • Class 12 Humanities
      • NCERT Solutions for Class 12 History
      • NCERT Solutions for Class 12 Political Science
      • NCERT Solutions for Class 12 Economics
      • NCERT Solutions for Class 12 Sociology
      • NCERT Solutions for Class 12 Psychology
  • Class 11
    • Class 11 Science
      • NCERT Solutions for Class 11 Maths
      • NCERT Solutions for Class 11 Physics
      • NCERT Solutions for Class 11 Chemistry
      • NCERT Solutions for Class 11 Biology
      • NCERT Solutions for Class 11 Economics
      • NCERT Solutions for Class 11 Computer Science (Python)
      • NCERT Solutions for Class 11 English
      • NCERT Solutions for Class 11 Hindi
    • Class 11 Commerce
      • NCERT Solutions for Class 11 Maths
      • NCERT Solutions for Class 11 Business Studies
      • NCERT Solutions for Class 11 Accountancy
      • NCERT Solutions for Class 11 Economics
      • NCERT Solutions for Class 11 Entrepreneurship
    • Class 11 Humanities
      • NCERT Solutions for Class 11 Psychology
      • NCERT Solutions for Class 11 Political Science
      • NCERT Solutions for Class 11 Economics
      • NCERT Solutions for Class 11 Indian Economic Development
  • Class 10
    • NCERT Solutions for Class 10 Maths
    • NCERT Solutions for Class 10 Science
    • NCERT Solutions for Class 10 Social Science
    • NCERT Solutions for Class 10 English
    • NCERT Solutions For Class 10 Hindi Sanchayan
    • NCERT Solutions For Class 10 Hindi Sparsh
    • NCERT Solutions For Class 10 Hindi Kshitiz
    • NCERT Solutions For Class 10 Hindi Kritika
    • NCERT Solutions for Class 10 Sanskrit
    • NCERT Solutions for Class 10 Foundation of Information Technology
  • Class 9
    • NCERT Solutions for Class 9 Maths
    • NCERT Solutions for Class 9 Science
    • NCERT Solutions for Class 9 Social Science
    • NCERT Solutions for Class 9 English
    • NCERT Solutions for Class 9 Hindi
    • NCERT Solutions for Class 9 Sanskrit
    • NCERT Solutions for Class 9 Foundation of IT
  • CBSE Sample Papers
    • Previous Year Question Papers
    • CBSE Topper Answer Sheet
    • CBSE Sample Papers for Class 12
    • CBSE Sample Papers for Class 11
    • CBSE Sample Papers for Class 10
    • Solved CBSE Sample Papers for Class 9 with Solutions 2024-2025
    • CBSE Sample Papers Class 8
    • CBSE Sample Papers Class 7
    • CBSE Sample Papers Class 6
  • Textbook Solutions
    • Lakhmir Singh
    • Lakhmir Singh Class 10 Physics
    • Lakhmir Singh Class 10 Chemistry
    • Lakhmir Singh Class 10 Biology
    • Lakhmir Singh Class 9 Physics
    • Lakhmir Singh Class 9 Chemistry
    • PS Verma and VK Agarwal Biology Class 9 Solutions
    • Lakhmir Singh Science Class 8 Solutions

Learn CBSE

NCERT Solutions for Class 6, 7, 8, 9, 10, 11 and 12

Algebraic Expressions and Identities Class 8 Notes Maths Chapter 9

January 24, 2024 by Sastry CBSE

CBSE Class 8 Maths Notes Chapter 9 Algebraic Expressions and Identities Pdf free download is part of Class 8 Maths Notes for Quick Revision. Here we have given NCERT Class 8 Maths Notes Chapter 9 Algebraic Expressions and Identities.

CBSE Class 8 Maths Notes Chapter 9 Algebraic Expressions and Identities

A symbol which takes various numerical values is called a variable.

A combination of constants and variables connected by the signs of fundamental operations of addition, subtraction, multiplication and division is called an algebraic expression.

Various parts of an algebraic expression which are separated by the signs of ‘+’ or ‘-‘ are called the terms of the expression.

An algebraic expression is called a monomial, a binomial, a trinomial, a quadrinomial accordingly as it contains one term, two terms, three terms and four terms, respectively.

While adding or subtracting polynomials, first look for like terms and then add or subtract these terms, then handle the, unlike terms.

Monomial multiplied by a monomial always gives a monomial.

While multiplying a polynomial by a monomial, we multiply every term in the polynomial by the monomial.

While multiplying a polynomial by a binomial (or trinomial), we multiply term by term, i.e., every term of a polynomial is multiplied by every term of in the binomial (or trinomial) and after that, we combined the like terms.

An identity is equality, which is true for all values of the variable in the equality.

The following are the useful identities and these identities are known as standard identities.

  • (a + b)2 = a2 + 2ab + b2
  • (a – b)2 = a2 – 2ab + b2
  • (a + b) (a – b) = a2 – b2
  • (x + a) (x + b) = x2 + (a + b) x + ab
  • (x + a) (x – b) = x2 + (a – b) x – ab
  • (x – a) (x + b) = x2 – (a – b) x – ab
  • If x is a variable and m, n are positive integers, then (xm × xn) = x(m+n) Thus, x2 × x4 = x(2+4) = x6
  • If x is a variable and m, n are positive integers such that m > n, then (xm ÷ xn) = xm-n. Thus, x9 ÷ x4 = x9-4 = x5
  • Product of two monomials = (Product of their coefficients) × (Product of their variables)
  • Division of two monomials = (Division of their coefficients) × (Division of their variables)

What are Expressions?
We know that a constant is a symbol having fixed numerical value whereas a variable is a symbol assuming various numerical values.
An algebraic expression is formed from variables and constants. A combination of variables and constants connected by the signs +, -, × and ÷ is called an algebraic expression. The variable/variables in an algebraic expression can assume countless different values. The value of algebraic expression changes with the value (s) assumed by the variable (s) it contains.

Terms, Factors and Coefficients
Terms are added to form expressions. Terms themselves can be formed as the product of factors. The numerical factor (with sign) of a term is called it’s coefficient.

Monomials, Binomials and Polynomials
An expression that contains exactly one, two or three terms is called a monomial, binomial or trinomial, respectively. In general, an expression containing, one or more terms with non-zero coefficients and with variable having non-negative exponents is called a polynomial.

Like and Unlike Terms
Like (or similar) terms are formed from the same variables and the powers of these variables are also the same. Coefficients of like terms need not be the same. In case otherwise, they are called, unlike (or dissimilar) terms.

Addition and Subtraction of Algebraic Expressions
While adding (or subtracting) polynomials, first look for like terms and add (or subtract) them; then handle the unlike terms. Note that the sum of a number of like terms is another like term whose coefficient is the sum of the coefficients of the like terms being added.

Multiplication of Algebraic Expressions Introduction
There exist a number of situations when we need to multiply algebraic expressions. For example, in finding area of a rectangle whose sides are given as expressions.

Multiplying a Monomial by a Monomial
A monomial multiplied by a monomial always gives a monomial.

Multiplying Two Monomials
In the product of two monomials
Coefficient = coefficient of the first monomial × coefficient of the second monomial
Algebraic factor = algebraic factor of a first monomial × algebraic factor of the second monomial

Multiplying Three or More Monomials
We first multiply the first two monomials and then multiply the resulting monomial by the third monomial. This method can be extended to the product of any number of monomials.

Rules of Signs
The product of two factors is positive or negative accordingly as the two factors have like signs or unlike signs. Note that
(i) (+) × (+) = +
(ii) (+) × (-) = –
(iii) (-) × (+) = –
(iv) (-) × (-) = +
If x is a variable and p, q are positive integers, then xp × xq = xp+q

Multiplying a Monomial by a Polynomial
While multiplying a polynomial by a monomial, we multiply every term in the polynomial by the monomial.

Multiplying a Monomial by a Binomial
By using the distributive law, we carry out the multiplication term by term.
It states that if P, Q and R are three monomials, then

  • P × (Q + R) = (P × Q) + (P × R)
  • (Q + R) × P = (Q × P) + (R × P)

Multiplying a Monomial by a Trinomial
By using the distributive law, we carry out the multiplication term by term.

Multiplying A Polynomial by a Polynomial
We multiply each term of one polynomial by each term of the other polynomial. Also, we combine the like terms in the product.

Multiplying a Binomial by a Binomial
We use distributive law and multiply each of the two terms of one binomial by each of the two terms of the other binomial and combine like terms in the product.
Thus, if P, Q, R and S are four monomials, then
(P + Q) × (R + S) = P × (R + S) + Q × (R + S)
= (P × R + P × S) + (Q × R + Q × S)
= PR + PS + QR + QS.

Multiplying a Binomial by a Trinomial
We use distributive law and multiply each of the three terms in the trinomial by each of the two terms in the binomial and combine like terms in the product.

What is Identity?
An identity is equality, which is true for all values of the variables, in the equality. On the other hand, an equation is true only for certain values of its variables. An equation is not always an identity. However, obviously, an identity is always an equation.

Standard Identities
(i) (a + b)2 = a2 + 2ab + b2
i.e., square of the sum of two terms = (square of the first term) + 2 × (first term) × (second term) + (square of the second term )

(ii) (a – b)2 = a2 – 2ab + b2
i.e., square of the difference of two terms = (square of the first term) – 2 × (first term) × (second term) + (square of the second term)

(iii) (a + b)(a – b) = a2 – b2
i.e., (first term + second term) (first term – second term) = (first term)2 – (second term)2

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

Applying Identities
The above identities are useful in carrying out squares and products of algebraic expressions. They provide us with easy alternative methods to calculate products of numbers and so on.

We hope the given CBSE Class 8 Maths Notes Chapter 9 Algebraic Expressions and Identities Pdf free download will help you. If you have any query regarding NCERT Class 8 Maths Notes Chapter 9 Algebraic Expressions and Identities, drop a comment below and we will get back to you at the earliest.

Filed Under: CBSE

LearnCBSE.in Student Education Loan
  • Student Nutrition - How Does This Effect Studies
  • Words by Length
  • NEET MCQ
  • Factoring Calculator
  • Rational Numbers
  • CGPA Calculator
  • TOP Universities in India
  • TOP Engineering Colleges in India
  • TOP Pharmacy Colleges in India
  • Coding for Kids
  • Math Riddles for Kids with Answers
  • General Knowledge for Kids
  • General Knowledge
  • Scholarships for Students
  • NSP - National Scholarip Portal
  • Class 12 Maths NCERT Solutions
  • Class 11 Maths NCERT Solutions
  • NCERT Solutions for Class 10 Maths
  • NCERT Solutions for Class 9 Maths
  • NCERT Solutions for Class 8 Maths
  • NCERT Solutions for Class 7 Maths
  • NCERT Solutions for Class 6 Maths
  • NCERT Solutions for Class 6 Science
  • NCERT Solutions for Class 7 Science
  • NCERT Solutions for Class 8 Science
  • NCERT Solutions for Class 9 Science
  • NCERT Solutions for Class 10 Science
  • NCERT Solutions for Class 11 Physics
  • NCERT Solutions for Class 11 Chemistry
  • NCERT Solutions for Class 12 Physics
  • NCERT Solutions for Class 12 Chemistry
  • NCERT Solutions for Class 10 Science Chapter 1
  • NCERT Solutions for Class 10 Science Chapter 2
  • Metals and Nonmetals Class 10
  • carbon and its compounds class 10
  • Periodic Classification of Elements Class 10
  • Life Process Class 10
  • NCERT Solutions for Class 10 Science Chapter 7
  • NCERT Solutions for Class 10 Science Chapter 8
  • NCERT Solutions for Class 10 Science Chapter 9
  • NCERT Solutions for Class 10 Science Chapter 10
  • NCERT Solutions for Class 10 Science Chapter 11
  • NCERT Solutions for Class 10 Science Chapter 12
  • NCERT Solutions for Class 10 Science Chapter 13
  • NCERT Solutions for Class 10 Science Chapter 14
  • NCERT Solutions for Class 10 Science Chapter 15
  • NCERT Solutions for Class 10 Science Chapter 16

Free Resources

RD Sharma Class 12 Solutions RD Sharma Class 11
RD Sharma Class 10 RD Sharma Class 9
RD Sharma Class 8 RD Sharma Class 7
CBSE Previous Year Question Papers Class 12 CBSE Previous Year Question Papers Class 10
NCERT Books Maths Formulas
CBSE Sample Papers Vedic Maths
NCERT Library

NCERT Solutions

NCERT Solutions for Class 10
NCERT Solutions for Class 9
NCERT Solutions for Class 8
NCERT Solutions for Class 7
NCERT Solutions for Class 6
NCERT Solutions for Class 5
NCERT Solutions for Class 4
NCERT Solutions for Class 3
NCERT Solutions for Class 2
NCERT Solutions for Class 1

Quick Resources

English Grammar Hindi Grammar
Textbook Solutions Maths NCERT Solutions
Science NCERT Solutions Social Science NCERT Solutions
English Solutions Hindi NCERT Solutions
NCERT Exemplar Problems Engineering Entrance Exams
Like us on Facebook Follow us on Twitter
Watch Youtube Videos NCERT Solutions App