The NCERT solutions for Class 8 CBSE include topics with frequent, focused, engaging challenges and activities that strengthen Math concepts. Each question of exercise 9.1 in NCERT Class 8 Maths Solutions has been carefully solved and helps you obtain the correct answer.
Class 8 Maths Chapter 9 Algebraic Expressions and Identities Exercise 9.1 questions and answers help students to understand polynomial 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 a step-by-step approach. Download free NCERT Solutions for Maths Chapter 9 and practise offline.
NCERT Solutions for Class 8 Maths Chapter 9 Algebraic Expressions and Identities Exercise 9.1
Access Answers of Maths NCERT Class 8 Chapter 9 Algebraic Expressions and Identities Exercise 9.1 Page number 140
Exercise 9.1 Page No: 140
- Identify the terms, their coefficients for each of the following expressions.
(i)Â 5xyz2Â – 3zy
(ii) 1 + x + x2
(iii)Â 4x2y2Â – 4x2y2z2Â + z2
(iv)Â 3 – pq + qr – p
(v) (x/2) + (y/2) – xy
(vi)Â 0.3a – 0.6ab + 0.5b
Solution :
| Sl. No. | Expression | Term | Coefficient |
| i) | 5xyz2Â – 3zy | Term:Â 5xyz2
Term: -3zy |
5 -3 |
| ii) | 1 + x + x2 | Term: 1 Term: x Term: x2 |
1 1 1 |
| iii) | 4x2y2Â – 4x2y2z2Â + z2 | Term:Â 4x2y2 Term:Â -4 x2y2z2 Term : Â z2 |
4 -4 1 |
| iv) | 3 – pq + qr – p | Term :Â 3 Term :Â -pq Term :Â qr Term :Â -p |
3 -1 1 -1 |
| v) | (x/2) + (y/2) – xy | Term :Â x/2 Term :Â Y/2 Term :Â -xy |
½ 1/2 -1 |
| vi) | 0.3a – 0.6ab + 0.5b | Term :Â 0.3a Term :Â -0.6ab Term :Â 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 + x2Â + x3Â + x4 | four terms | Polynomial, and it does not fit in the 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 the listed three categories |
| pqr | one term | Monomial |
| p2q + pq2 | two terms | Binomial |
| 2p + 2q | two terms | Binomial |
| 7+y+5x | three terms | Trinomial |
3. Â Add the following.
(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)Â l2Â + m2, m2Â + n2, n2Â + 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
= (2p2q2Â – 3pq + 4) + (5 + 7pq – 3p2q2)
= 2p2q2Â – 3p2q2Â – 3pq + 7pq + 4 + 5
= – p2q2Â + 4pq + 9
iv)Â (l2Â + m2) + (m2Â + n2) + (n2Â + l2) + (2lm + 2mn + 2nl)
=Â l2Â + l2Â + m2Â + m2Â + n2Â + n2Â + 2lm + 2mn + 2nl
=Â 2l2Â + 2m2Â + 2n2Â + 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
=Â 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 – 2pq2Â + 5p2q) – (4p2q – 3pq + 5pq2Â – 8p + 7q – 10)
= 18 – 3p – 11q + 5pq – 2pq2Â + 5p2q – 4p2q + 3pq – 5pq2Â + 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 – 7pq2Â + 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, and addition and subtraction of algebraic expressions. The operations like addition and subtraction are mainly performed on monomials, binomials and polynomials. After practising these questions, students will become confident about the concept and able to solve problems on their own.
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