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Class 8 RD Sharma Solutions – Chapter 6 Algebraic Expressions And Identities – Exercise 6.1
  • Difficulty Level : Expert
  • Last Updated : 24 Nov, 2020

Question 1. Identify the terms, their coefficients for each of the following expressions:

(i) 7x2yz – 5xy

(ii) x2 + x + 1

(iii) 3x2y2 – 5x2y2z2 + z2

(iv) 9 – ab + bc – ca

(v) a/2 + b/2 – ab



(vi) 0.2x – 0.3xy + 0.5y

Solution:

(i) 7x2yz – 5xy

In this expression there are two terms:

7x2yz and – 5xy

The coefficient of 7x2yz is 7

The coefficient of –5xy is –5

(ii) x2 + x + 1

In this expression there are three terms:

x2, x and 1

The coefficient of x2  is 1

The coefficient of x is 1

The coefficient of 1 is 1

(iii) 3x2y2 – 5x2y2z2 + z2

In this expression there are  three terms:

3x2y, -5x2y2z2 and z2

The coefficient of 3x2y is 3

The coefficient of -5x2y2z2 is -5



The coefficient of z2 is 1

(iv) 9 – ab + bc – ca

In this expression there are four terms:

9, -ab, bc and -ca

The coefficient of 9 is 9

The coefficient of -ab is -1

The coefficient of bc is 1

The coefficient of -ca is -1

(v) a/2 + b/2 – ab

In this expression there are three terms:

a/2, b/2, and -ab

The coefficient of a/2 is 1/2

The coefficient of b/2 is 1/2

The coefficient of -ab is -1

(vi) 0.2x – 0.3xy + 0.5y

In this expression there are three terms:

0.2x, -0.3xy and 0.5y

The coefficient of 0.2x is 0.2

The coefficient of -0.3xy is -0.3

The coefficient of 0.5y is 0.5



Question 2. Classify the following polynomials as monomials, binomials, trinomials. Which polynomials do not fit in any category?

(i) x + y

(ii) 1000

(iii) x + x2 + x3 + x4

(iv) 7 + a + 5b

(v) 2b – 3b2

(vi) 2y – 3y2 + 4y3

(vii) 5x – 4y + 3x

(viii) 4a – 15a2

(ix) xy + yz + zt + tx

(x) pqr

(xi) p2q + pq2

(xii) 2p + 2q

Solution:

(i) x + y

The given expression contains two terms x and y

∴ It is Binomial

(ii) 1000

The given expression contains one term 1000

∴ It is Monomial

(iii) x + x2 + x3 + x4

The given expression contains four terms

∴ It belongs to none of the categories

(iv) 7 + a + 5b

The given expression contains three terms

∴ It is Trinomial

(v) 2b – 3b2

The given expression contains two terms

∴ It is Binomial

(vi) 2y – 3y2 + 4y3

The given expression contains three terms

∴ It is Trinomial

(vii) 5x – 4y + 3x

The given expression contains three terms

∴ It is Trinomial

(viii) 4a – 15a2

The given expression contains two terms

∴ It is Binomial

(ix) xy + yz + zt + tx

The given expression contains four terms

∴ It belongs to none of the categories

(x) pqr

The given expression contains one term

∴ It is Monomial

(xi) p2q + pq2

The given expression contains two terms

∴ It is Binomial

(xii) 2p + 2q

The given expression contains two terms

∴ It is Binomial

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