Students can refer to the PDF of RD Sharma Solutions for Class 8 Maths Exercise 6.1 Chapter 6, Algebraic Expressions and Identities, which is designed by our expert team. RD Sharma Solutions is one of the best reference materials for CBSE students, and they can download the PDF from the links provided below. In Exercise 6.1 of Chapter 6, Algebraic Expressions and Identities, we will discuss the basic definitions used in algebra, like constants, variables, algebraic expressions, monomials, binomials, trinomials, factors and coefficients.
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, and 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 and trinomials. Which polynomials do not fit into 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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