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

NCERT Solutions for Class 8 Maths Chapter 9 Exercise 9.1

Question 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 - rp
(v) (x/2) -(y/2) -xy
(vi)0.3a - 0.6ab + 0.5b
Answer


Question 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
Answer
x + y: Binomial
1000: Monomial
x + x²+ x³+ x⁴:Polynomial
7 + y + 5x:Binomial
2y - 3y²: Binomial
2y - 3y²+ 4y³: Trinomial
5x - 4y + 3xy:Trinomial
4z - 15z²: Binomial
ab + bc + cd + da:Polynomial
pqr:Monomial
p²q + pq²: Binomial
2p + 2q:Binomial


Question 3
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)l² + m², m²+ n², n²+ l², 2lm + 2mn + 2nl
Answer (i) (ab - bc) + (bc - ca) + (ca-ab)
= ab + bc + ca - bc - ca - ab
= 0
(ii) (a - b + ab) + (b - c + bc) + (c - a + ac)
= a + b + c + ab + bc + ca - b - c - a
= 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

Question 4.
(a) Subtract 4a - 7ab + 3b + 12 from 2a - 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
Answer: While subtracting, we need to remember signs are reversed after -sign once bracket is opened
ie. + becomes - and - becomes +
Let solve the below question keeping that in mind
(a) (12a - 9ab + 5b - 3) - (4a - 7ab + 3b + 12)
= 12a - 9ab + 5b - 3 - 4a + 7ab - 3b - 12
=8a - 2ab + 2b - 15
(b) (5xy - 2yz - 2zx + 10xyz) - (3xy + 5yz - 7zx)
= 5xy - 2yz - 2zx + 10xyz - 3xy - 5yz + 7zx
= 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
= 28 + 5p - 18q + 8pq - 7pq² - p²q

Summary

1. NCERT Solutions for Class 8 Maths Chapter 9 Algebraic Expressions and Identities Exercise 9.1 has been prepared by Expert with utmost care. If you find any mistake.Please do provide feedback on mail. You can download the solutions as PDF in the below Link also
   Download Algebraic Expressions Exercise 9.1 as pdf
2. This chapter 9 has total 5 Exercise 9.1 ,9.2 ,9.3 ,9.4 and 9.5. This is the First exercise in the chapter.You can explore previous exercise of this chapter by clicking the link below

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• Notes
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• Ncert Solutions
  • NCERT Solutions for Class 8 Maths Chapter 9 Algebraic Expressions and Identities Exercise 9.1
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