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RD Sharma Class 8 Solutions Chapter 6 - Algebraic Expressions and Identities (Ex 6.2) Exercise 6.2

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Last updated date: 17th May 2024
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RD Sharma Class 8 Solutions Chapter 6 - Algebraic Expressions and Identities (Ex 6.2) Exercise 6.2 - Free PDF

Download the free PDF of RD Sharma Class 8 Solutions of Chapter 6 - Algebraic Expressions and Identities. Exercise 6.2 is solved by Expert Mathematics Teachers on Vedantu.com. All Chapter 6 - Algebraic Expressions and Identities. Ex 6.2 Questions with Solutions for RD Sharma Class 8 Math to help in revising the complete Syllabus and Score More marks. Register for online coaching for IIT JEE (Mains & Advanced) and other engineering entrance exams. One can also register Online for Class 8 Science tuition on Vedantu.com to score more marks in the CBSE board examination. Vedantu is a platform that provides free CBSE Solutions (NCERT) and other study materials for students.

Introduction to the Chapter

The sixth Chapter of RD Sharma Class 8 Solutions is ‘Algebraic Expressions and Identities’. In the Chapter ‘Algebraic Expressions and Identities’, the students will learn about various expressions which consist of variables, constants, and mathematical operations such as addition, subtraction, division, and multiplication. Algebraic Expressions can be monomial, binomial, or polynomial which means representing one term, two terms, or more than two terms combined by mathematical operations respectively. 


Students in the Chapter ‘Algebraic Expressions and Identities’ learn about many terms like coefficients, terms, factors, like and unlike terms, identity, standard identities, and mathematical operations on algebraic expressions.


Sections of RD Sharma Class 8 Chapter 6- Algebraic Expressions and Identities

Topics

Sub-Topics

What are expressions?


Terms, Factors, and Coefficients


Monomials, Binomials and Polynomials


Like and Unlike Terms


Addition and Subtraction of Algebraic Expressions


Multiplication of Algebraic Expressions

Introduction

Multiplying a monomial by a monomial

Multiplying two monomials

Multiplying three or more monomials

Multiplying a monomial by a polynomial

Multiplying a monomial by a polynomial

Multiplying a monomial by a trinomial

Multiplying a polynomial by a polynomial

Multiplying a binomial by a binomial

Multiplying a binomial by a trinomial

What is an Identity?


Standard Identities


Applying Identities



Things to remember in Class 8 Chapter- Algebraic Expressions and Identities

  • Variables and Constants form expressions.

  • Terms are added in order to form expressions.

  • Terms are formed as a product of factors.

  • The expressions containing one, two, or three terms are called monomials, binomials, and trinomials respectively.

  • The expressions containing more than one term are known as polynomials.

  • There is no need for the coefficients of like terms to be the same.

  • Like terms can only be added or subtracted, while unlike terms cannot be added or subtracted.

  • A monomial when multiplied by a monomial always gives a monomial.

  • When a polynomial is multiplied by a monomial, every term in the polynomial is to be multiplied with the monomial.

  • Standard identities allow easier alternative methods to calculate the products of numbers and so on.

FAQs on RD Sharma Class 8 Solutions Chapter 6 - Algebraic Expressions and Identities (Ex 6.2) Exercise 6.2

1. Apply standard Identities on the following equations.
A.(2x + 3y)2
B.(103)2

For A 

Using (a + b)2 = a2 + b2 +2ab

(2x + 3y)2 = (2x)2 + 2(2x)(3y) + (3y)2 = 4x2 + 12xy + 9y2

For B 

Using (a + b)2 = a2 + b2 + 2ab

(103)2 = (100 + 3)2 = 1002 + 2 x 100 x 3 +32 = 10000 + 600 + 9 = 10609

2. Where can one find the study material for Algebraic Expression?

Algebraic Equations and Identities is an important chapter in Class 8, as it lays a foundation for future concepts of Algebra in higher classes. Therefore, it is very important for students to have a strong command of this chapter and a clear picture of each and every concept in this chapter. For reference, Vedantu has provided study notes for the Chapter Algebraic Expressions and Identities in a step-by-step and easy-to-understand manner. After going through the notes the student will have all his doubts cleared regarding algebraic equations as the notes are specially designed by subject experts for the ease of students.

3. What are the properties of Algebraic Equations?

There are 9 properties of Algebraic equations which are as follows-

  • Commutative Property of Addition- The commutative property of addition states that regardless of the order of any two numbers while adding, the sum remains the same, that is, x+y=y+x.

  • Commutative Property of Multiplication- The commutative property of multiplication states that regardless of the order of two numbers while multiplying, the product remains the same, that is, x x y=y x x.

  • Associative Property of Addition- The associative property of addition states that regardless of sets of grouping together of two numbers while adding, the sum remains the same, that is, x+(y+z)=(x+y)+z.

  • Associative Property of Multiplication- The associative property of multiplication states that regardless of sets of grouping together of two numbers while multiplying, the product remains the same, that is, x x (y x z)=(x x y) x z.

  • Distributive Property- The distributive property of algebraic equations states that equality is always true in elementary algebra. Distributive property generalized the distributive law, that is, x x (y±z)=(x x y)±(x x z).

  • Identity property for addition- The identity property of addition states that the number remains the same if zero is added to it, that is, x+0=x.

  • Identity property for multiplication- The identity property of multiplication states that if 1 is multiplied by any number, the number remains the same, that is, x 1=x

  • Inverse property of addition- The inverse property of addition states that whenever a number and its opposite is added, for example, 2 and -2, the result will always be 0, that is, x+(-x)=0.

  • Zero Property of Multiplication- The zero property of multiplication states that whenever we multiply any number by 0, the product will always be a 0, that is x 0=0.