In this page we have NCERT Solutions for Class 8 Maths Chapter 9 Algebraic Expressions and Identities for
Exercise 9.1. This exercise has question about Terms, Factors and Coefficient, Addition & subtraction of polynomials, type of polynomials and Like and Unlike Term. Hope you like them and do not forget to like , social share
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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)5xyz
^{2}- 3zy
(ii)1 + x + x
^{2}
(iii)4x
^{2}y
^{2}- 4x
^{2}y
^{2}z
^{2}+ z
^{2}
(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 + x
^{2} + x
^{3}+ x
^{4}
7 + y + 5x
2y - 3y
^{2}
2y - 3y
^{2}+ 4y
^{3}
5x - 4y + 3xy
4z - 15z
^{2}
ab + bc + cd + da
pqr
p
^{2}q + pq
^{2}
2p + 2q
Answer
x + y: Binomial
1000: Monomial
x + x
^{2}+ x
^{3}+ x
^{4}:Polynomial
7 + y + 5x:Binomial
2y - 3y
^{2}: Binomial
2y - 3y
^{2}+ 4y
^{3}: Trinomial
5x - 4y + 3xy:Trinomial
4z - 15z
^{2}: Binomial
ab + bc + cd + da:Polynomial
pqr:Monomial
p
^{2}q + pq
^{2}: 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)2p
^{2}q
^{2}- 3pq + 4, 5 + 7pq - 3p
^{2}q
^{2}
(iv)l
^{2} + m
^{2}, m
^{2}+ n
^{2}, n
^{2}+ l
^{2}, 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) 2p
^{2}q
^{2}- 3pq + 4, 5 + 7pq - 3p
^{2}q
^{2}
= (2p
^{2}q
^{2}- 3pq + 4) + (5 + 7pq - 3p
^{2}q
^{2})
= 2p
^{2}q
^{2}- 3p
^{2}q
^{2} - 3pq + 7pq + 4 + 5
= - p
^{2}q
^{2}+ 4pq + 9
(iv) (l
^{2}+ m
^{2}) + (m
^{2}+ n
^{2}) + (n
^{2}+ l
^{2}) + (2lm + 2mn + 2nl)
=l
^{2}+ l
^{2}+ m
^{2}+ m
^{2}+ n
^{2}+ n
^{2}+ 2lm + 2mn + 2nl
=2l
^{2}+ 2m
^{2}+ 2n
^{2}+ 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 4p
^{2}q - 3pq + 5pq
^{2}- 8p + 7q - 10
from 18 - 3p - 11q + 5pq - 2pq
^{2}+ 5p
^{2}q
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 - 2pq
^{2} + 5p
^{2}q) - (4p
^{2}q - 3pq + 5pq
^{2} - 8p + 7q - 10)
= 18 - 3p - 11q + 5pq - 2pq
^{2} + 5p
^{2}q - 4p
^{2}q + 3pq - 5pq
^{2} + 8p - 7q + 10
= 28 + 5p - 18q + 8pq - 7pq
^{2} - p
^{2}q
Summary
- 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
- 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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