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RS Aggarwal Solutions Class 8 Chapter-6 Operations on Algebraic Expressions (Ex 6D) Exercise 6.4

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Last updated date: 22nd Mar 2024
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MVSAT 2024

RS Aggarwal Solutions Class 8 Chapter-6 Operations on Algebraic Expressions (Ex 6D) Exercise 6.4 - Free PDF

Maths is a subject that deals with numbers. If a student is familiar with numbers, it will improve his/her problem-solving and analytical skills considerably. Algebra plays an essential role in maths. The algebraic expressions involve variables, basic operations such as addition, subtraction, multiplication, and division. These operations can be performed using certain laws and basic formulas which should be remembered. 

Chapter 6- Operations on Algebraic Expressions

In this chapter, you will learn how to add, subtract, multiply and divide algebraic expressions. This chapter consists of important algebraic identities that will not only help you in Class 8 but will be useful in higher classes. This chapter is divided into 5 exercises (Exercise- 6A, 6B, 6C, 6D, 6E) and consists of 95 questions overall. 

  • Exercise 6A consists of 20 questions and deals with the concept of addition and subtraction of polynomials. 

  • Exercise 6B consists of 26 questions and deals with the product of polynomials. 

  • Exercise 6C consists of 15 questions and deals with the concept of finding the remainder and quotient after dividing the given polynomials. 

  • Exercise 6D consists of 15 questions, where you have to evaluate the given algebraic expressions, expand the given algebraic expressions, and use the formula for squaring a binomial and evaluate the given algebraic expressions. 

  • Exercise 6E consists of 19 questions and is based on algebraic identities. It is one of the easiest exercises, where you have to find the product of algebraic expressions. 

Conclusion

To learn these concepts of algebraic expressions in an easy manner with in-depth understanding, Vedantu provides RS Aggarwal Solution for Class 8 Chapter 6- Operations on Algebraic Expressions, (Ex-65D) Exercise 6.4- PDF for free.

FAQs on RS Aggarwal Solutions Class 8 Chapter-6 Operations on Algebraic Expressions (Ex 6D) Exercise 6.4

1. How Vedantu’s RS Aggarwal Solutions Class 8 Chapter-6 Operations on Algebraic Expressions (Ex 6D) Exercise 6 helps students?

Vedantu’s RS Aggarwal Solutions are the perfect study material for the students of Class 8. These solutions are written in very simple language for a better understanding of concepts. The solutions provided by us will help you in gaining knowledge and create a strong foundation with the concepts and help students to score more marks in the final exam. Regular practice of topics will help students write the exams with more confidence.

2. What are the steps for the addition of algebraic expressions according to RS Aggarwal Solutions Class 8 Chapter-6 Operations on Algebraic Expressions (Ex 6D) Exercise 6?

Adding algebraic expression consist of  step by step procedure, they are listed below:

  • Step 1: Sort out all the like terms based on the variables, i.e., group all the same variable terms.

  • Step 2: Perform addition on all the grouped terms with the same variables by adding the coefficients and should be written in a single coefficient term.

  • Step 3: Similarly, perform operations for all the like terms.

  • Step 4: The addition of constants should be done like the usual addition of numbers.

  • Step 5: If no like terms are present, then keep the expression as it is.

3. What are the steps for the multiplication of algebraic expressions mentioned in RS Aggarwal Solutions Class 8 Chapter-6 Operations on Algebraic Expressions (Ex 6D) Exercise 6?

In the multiplication of algebraic expressions, there are two simple rules,

(i) The product of two terms with like (same) signs are positive. The product of two terms with unlike (different) signs are negative.

(ii) If x is a variable and m, n are positive integers, then (xm×xn)=xm+n.

Following are the steps for multiplication of algebraic expressions:

  • Step 1: Multiply each term of the first expression with each term of the second expression.

  • Step 2: If the same variables appear, add the powers and express them as exponents with the variable.

  • Step 3: Write as the product of another variable, if there are different variables.

  • Step 4: After Multiplication separate every term obtained by its respective signs.

4. What are the important algebraic identities according to RS Aggarwal Solutions Class 8 Chapter-6 Operations on Algebraic Expressions (Ex 6D) Exercise 6?

The following are some of the important algebraic identities

  • a2b2= (a - b) (a + b)

  • (a + b)2= a2 + 2ab + b2

  • (a - b)2= a2 − 2ab + b2

  • (a + b + c)2= a2 + b2 + c2 + 2ab+ 2bc + 2ca

  • (a + b)3= a3 + 3a2b + 3ab2 + b3 = a3 + b3 + 3ab (a + b)

  • (a - b)3= a3 − 3a2b + 3ab2b3 = a3b3 − 3ab ((a - b)

  • a3b3= (a - b) (a2 + ab + b2)

  • a3 + b3= (a + b) (a2ab + b2)

  • a3 + b3 + c3 − 3abc = (a + b + c)(a2 + b2 + c2abbcca)