 # NCERT Solutions for class 8 Maths Chapter 9 Algebraic Expressions and Identities Exercise 9.1

The NCERT solutions for Class 8 CBSE enhance topics with frequent, focused, engaging math challenges and activities that strengthen math concepts. Each question of the exercise has been carefully solved and you get the correct answer.

Class 8 Maths Chapter 9 Algebraic Expressions and Identities Exercise 9.1 questions and answers helps students to understand polynomial’s terms, factors and coefficients as well as addition and subtraction of the polynomials. NCERT Solutions for Class 8 Maths Chapter 9 Algebraic Expressions and Identities exercise 9.1 are prepared by BYJU’S subject experts using step by step approach. Download free NCERT Solutions for Maths Chapter 9 and practice offline.

### Download PDF of NCERT Solutions for Class 8 Maths Chapter 9 Algebraic Expressions and Identities Exercise 9.1   ## Exercise 9.1 Page No: 140

1. Identify the terms, their coefficients for each of the following expressions.
(i) 5xyz2 – 3zy
(ii) 1 + x + x2
(iii) 4x2y2 – 4x2y2z2 + z2
(iv) 3 – pq + qr – p
(v) (x/2) + (y/2) – xy
(vi) 0.3a – 0.6ab + 0.5b

Solution :

 Sl. No. Expression Term Coefficient i) 5xyz2 – 3zy Term: 5xyz2  Term: -3zy 5 -3 ii) 1 + x + x2 Term: 1 Term: xTerm x2 1 1 1 iii) 4x2y2 – 4x2y2z2 + z2 Term: 4x2y2 Term: -4 x2y2z2Term :  z2 4 -4 1 iv) 3 – pq + qr – p 3 -pq qr -p 3 -1 1 -1 v) (x/2) + (y/2) – xy x/2 Y/2 -xy ½ 1/2 -1 vi) 0.3a – 0.6ab + 0.5b 0.3a -0.6ab 0.5b 0.3 -0.6 0.5

2. Classify the following polynomials as monomials, binomials, trinomials. Which polynomials do not fit in any of these three categories?
x + y, 1000, x + x2 + x3 + x4 , 7 + y + 5x, 2y – 3y2 , 2y – 3y2 + 4y3 , 5x – 4y + 3xy, 4z – 15z2 , ab + bc + cd + da, pqr, p2q + pq2 , 2p + 2q

Solution:

Let us first define the classifications of these 3 polynomials:

Monomials, Contain only one term.

Binomials, Contain only two terms.

Trinomials, Contain only three terms.

 x + y two terms Binomial 1000 one term Monomial x + x2 + x3 + x4 four terms Polynomial, and it does not fit in listed three categories 2y – 3y2 two terms Binomial 2y – 3y2 + 4y3 three terms Trinomial 5x – 4y + 3xy three terms Trinomial 4z – 15z2 two terms Binomial ab + bc + cd + da four terms Polynomial, and it does not fit in listed three categories pqr one term Monomial p2q + pq2 two terms Binomial 2p + 2q two terms Binomial

(i) ab – bc, bc – ca, ca – ab
(ii) a – b + ab, b – c + bc, c – a + ac
(iii) 2p2q2 – 3pq + 4, 5 + 7pq – 3p2q2
(iv) l2 + m2, m2 + n2, n2 + l2, 2lm + 2mn + 2nl

Solution:

i) (ab – bc) + (bc – ca) + (ca-ab)
= ab – bc + bc – ca + ca – ab
= ab – ab – bc + bc – ca + ca

= 0

ii) (a – b + ab) + (b – c + bc) + (c – a + ac)
= a – b + ab + b – c + bc + c – a + ac

= a – a +b – b +c – c + ab + bc + ca

=0 + 0 + 0 + ab + bc + ca

= ab + bc + ca

iii) 2p2q2 – 3pq + 4, 5 + 7pq – 3p2q2
= (2p2q2 – 3pq + 4) + (5 + 7pq – 3p2q2)
= 2p2q2 – 3p2q2 – 3pq + 7pq + 4 + 5
= – p2q2 + 4pq + 9

iv)  (l2 + m2) + (m2 + n2) + (n2 + l2) + (2lm + 2mn + 2nl)
= l2 + l2 + m2 + m2 + n2 + n2 + 2lm + 2mn + 2nl
= 2l2 + 2m2 + 2n2 + 2lm + 2mn + 2nl

4. (a) Subtract 4a – 7ab + 3b + 12 from 12a – 9ab + 5b – 3

(b) Subtract 3xy + 5yz – 7zx from 5xy – 2yz – 2zx + 10xyz

(c) Subtract 4p2q – 3pq + 5pq2 – 8p + 7q – 10 from 18 – 3p – 11q + 5pq – 2pq2 + 5p2q

Solution:

(a) (12a – 9ab + 5b – 3) – (4a – 7ab + 3b + 12)

= 12a – 9ab + 5b – 3 – 4a + 7ab – 3b – 12

= 12a – 4a -9ab + 7ab +5b – 3b -3 -12

= 8a – 2ab + 2b – 15

b) (5xy – 2yz – 2zx + 10xyz) – (3xy + 5yz – 7zx)

= 5xy – 2yz – 2zx + 10xyz – 3xy – 5yz + 7zx

=5xy – 3xy – 2yz – 5yz – 2zx + 7zx + 10xyz

= 2xy – 7yz + 5zx + 10xyz

c) (18 – 3p – 11q + 5pq – 2pq2 + 5p2q) – (4p2q – 3pq + 5pq2 – 8p + 7q – 10)

= 18 – 3p – 11q + 5pq – 2pq2 + 5p2q – 4p2q + 3pq – 5pq2 + 8p – 7q + 10

=18+10 -3p+8p -11q – 7q + 5 pq+ 3pq- 2pq^2 – 5pq^2 + 5 p^2 q – 4p^2 q

= 28 + 5p – 18q + 8pq – 7pq2 + p2q

### Access other exercise solutions of class 8 Maths Chapter 9 Algebraic Expressions and Identities

Exercise 9.2 Solutions : 5 Questions (Short answers)

Exercise 9.3 Solutions : 5 Questions (Short answers)

Exercise 9.4 Solutions : 3 Questions (Short answers)

Exercise 9.5 Solutions : 8 Questions (Short answers)

### NCERT Solutions for class 8 Maths Chapter 9 Algebraic Expressions and Identities Exercise 9.1

This exercise of class 8 Maths Chapter 9 Algebraic Expressions and Identities is based on the polynomial terms, factors and coefficients, addition and subtraction of algebraic expressions. Addition and Subtraction operations are mainly performed on monomials, binomials and on polynomials. After practicing these questions students will get confident about the concept and able to solve problems at their own.