RD Sharma Solutions for Class 8 Maths Exercise 6.1 Chapter 6 Algebraic Expressions and Identities

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EXERCISE 6.1 PAGE NO: 6.2

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

The given equation has two terms that are:

7x2yz and – 5xy

The coefficient of 7x2yz is 7

The coefficient of – 5xy is – 5

(ii) x2 + x + 1

The given equation has three terms that are:

x2, x, 1

The coefficient of x2 is 1

The coefficient of x is 1

The coefficient of 1 is 1

(iii) 3x2y2 – 5x2y2z2 + z2

The given equation has three terms that are:

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

The given equation has four terms that are:

9, -ab, bc, -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

The given equation has three terms that are:

a/2, b/2, -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

The given equation has three terms that are:

0.2x, -0.3xy, 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

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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