RD Sharma Class 8 Solutions Chapter 6 - Algebraic Expressions and Identities (Ex 6.1) Exercise 6.1

Solutions to RD Sharma Class 8 Chapter 6 Algebraic Expressions and identities have been provided here. This chapter has included examples based on the topic of Algebraic Expressions and identities to solve real-life problems. In this chapter, students will understand the meaning and the concept of algebraic expressions. This chapter mainly deals with Algebraic Expressions and identities. In this chapter, we will be learning Algebraic Expressions and identities in detail.

Some Topics which have been discussed in this Chapter:

• 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 a Monomial by a Polynomial

• Multiplying a Polynomial by a Polynomial

• What is an Identity?

• Standard Identities

• Applying Identities

What are Expressions?

Variables and constants make expressions. The expression 7y – 8 is made from the variable y and constants 7 and 8. The expression mn + 7 has variables m and n and constants 7. When the value chosen for the variables an expression changes, the value of expression changes. Therefore, the value of 7y – 8 changes, as y takes on various values.

Terms, Factors and Coefficients

Let us take the example of 7x + 8. 

This expression has two terms, 7x and 8. 

Expressions are made up by adding terms. 

Terms can be represented as the product of factors. The term 7x is the product of the factors 7 and x. The term 8

has just one factor, i.e., 8.

The numerical factor of a term is known as its numerical coefficient.

Monomials, Binomials and Polynomials

Monomials are expressions that are made up of only one term. 

Some examples of monomials: 8x^{2},7y^{8} etc.

Binomials contain two terms.

Some examples of binomials: x+y, 8x^{2}+7y^{8} etc. 

Trinomial contains three terms and so on.

Some examples of trinomials: x + 7y –8, 8x^{2}+7y^{8}+z etc.

A polynomial is an expression having one or more terms with a non-zero coefficient. Thus, monomials, binomials, trinomials, etc., are all polynomials.

Some examples of polynomials: w+x+y+z, 7xy, 17y^{3} etc.

Like and Unlike Terms

Terms are considered to be like when:

• They have the same variables.

• The powers of these variables are the same. 

It is not necessary for the coefficients of like terms to be the same.

If the above conditions are not met, they are considered, unlike terms.

Addition and Subtraction of Algebraic Expressions

Let us learn how to add and subtract algebraic expressions.

To add or subtract polynomials, we add or subtract the like terms; then manage the, unlike terms.

Example : Add: 7pq + 8qr – 3rp, 4qr + 8rp – 3q.

Solution: To do addition the expressions to be added have to be written in separate rows. We put the like terms one below the other and then add or subtract them.

Let us write the expressions in separate rows, with like terms one below

the other 

  7pq + 8qr – 3rp+0q

+ 0pq+4qr + 8rp – 3q

_________________

7pq+12qr+5rp-3q

Hence, the sum is 7pq+12qr+5rp-3q .

Multiplication of Algebraic Expressions: Introduction

• Multiplying a Monomial by a Monomial

When a monomial is multiplied by a monomial we always get a monomial.

• Multiplying a Monomial by a Polynomial

To multiply a monomial by a polynomial, we have to multiply every term in the polynomial by the monomial.

• Multiplying a Polynomial by a Polynomial

When polynomials are multiplied with polynomials, it’s advisable to look out for like terms and combine them, if any.

What is an Identity?

An identity is an equality that holds true for every value of the variable.

An equation is not true for all values of the variable. It is true for only some values of the variable. 

Standard Identities

Here are some important identities that will be helpful to remember:

(a + b)^{2}= a^{2}+ 2ab + b^{2}

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

(a + b) (a – b) = a^{2}– b^{2}

These  identities are standard identities.

(x + a) (x + b) = x^{2}+ (a + b) x + ab

The above identity is the general form of the other three identities.

Applying Identities

The above four identities are mostly used in finding out squares and products of algebraic expressions. 

Conclusion

For students wishing to score stellar grades in Math, RD Sharma Solutions is the best study material. Our subject matter experts at Vedantu have prepared the  RD Sharma solutions to help the students who find difficulties in solving them. Students can easily access answers to the problems present in RD Sharma Class 8 Chapter 6 by downloading the PDF. It contains all the solutions in a detailed manner and also expects questions to be asked in the exam. After solving these questions students will surely get more confident about the exam.