Class 8 NCERT Solutions Chapter 9 Algebraic Expressions and Identities Exercise 9.1 (original) (raw)
Last Updated : 7 Aug, 2024
**Question 1. Identify the terms, their coefficients for each of the following expressions.
**Need to be Known:
- **Expression: An Expression is the addition of terms. Example: **7y + z is an expression made up of two terms **7y and **z.
- **Term: Terms itself is a product of factors. Example: **7y + z, here terms are **7y (term 1) and **z (term2) where **term 1 is the product of two factors **7 and **y . and **term 2 is a single factor **z.
- **Coefficient: It is a numerical factor of the term. Example: **7y + z here **term1 has a two factor 7 and **y in which 7 is numerical factor hence it is a coefficient.
****(i) 5xyz** 2 **- 3zy
**Solution:
- Here terms are 5xyz2 and -3zy
- Here Coefficients are 5 and -3
****(ii) 1 + x + x** 2
**Solution:
- Here terms are 1, x, x2
- Here Coefficients are 1, 1, 1
****(iii) 4x** 2 y 2 **– 4x 2 y 2 z 2 **+ z 2
**Solution:
- Here terms are 4x2y2, –4x2y2z2 and z2
- Here Coefficients are 4, -4 and 1
****(iv)** **3 – pq + qr – rp
**Solution:
- Here terms are -3, -pq, qr, -rp
- Here Coefficients are 3, -1, 1 and -1
****(v)** **x/2 + y/2 - xy
**Solution:
- Here terms are x/2, y/2 and -xy
- Here Coefficients are 1/2, 1/2 and -1
****(vi) 0.3a – 0.6ab + 0.5b**
**Solution:
- Here terms are 0.3a, -0.6ab and 0.5b
- Here Coefficients are 0.3, -0.6 and 0.5
**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
**Need to be Known:
- **Monomial: Expression made up of one term is known as monomial. Example: pqr, z, ab etc.
- **Binomial: Expression made up of two terms is known as binomial. Example: 2y + 3z, 5x - 4y, etc.
- **Trinomial: Expression made up of three terms is known as trinomial. Example: 2y + 3z + x, 5x - 4y + a, etc.
- **Polynomial: Expression made up of one or more terms is known as a polynomial. Example: a + b + c + d, 3xy, 7xyz – 10, 2x + 3y + 7z, etc
**Solution:
In this question:
- **Monomials: 1000, pqr
- **Binomials: x + y, 2y – 3y2, 4z – 15z2, p2q + pq2, 2p + 2q
- **Trinomials: 7 + y + 5x, 2y – 3y2+ 4y3, 5x – 4y + 3xy
- **and those which do not fit in these categories are: x + x2+ x3+ x4, ab + bc + cd + da
**Question 3. Add the following
**Need to be Known:
**Like term: Terms having the same variable with their same power.
**Note**: Terms those are like can only add and subtract each other. unlike terms cannot add and subtract each other. Example: 4x and 5x are like terms as they both have the same coefficient with the same power of x as 1.
**Unlike term: Terms having different variable and may have different powers.
- Example: 4x and 5y are unlike terms as they both have different variables
- Example: 4x2 and 5x3 are unlike terms as they both terms differ in the variable power.
****(i) ab – bc, bc – ca, ca – ab**
**Solution:
As here three expressions are given, we need to place expressions same terms below other expressions same term one by one then we will get like these:
ab - bc + 0
+ 0 + bc - ca
+ -ab + 0 + ca
_________________
0 + 0 + 0 <----------final expression
_________________
this tends to 0.
****(ii) a – b + ab, b – c + bc, c – a + ac**
**Solution:
As here three expressions are given, we need to place expressions same terms below other expressions same term one by one then we will get like these:
a – b + ab
+ 0 + b + 0 - c + bc
+ -a + 0 + 0 + c + 0 + ac
__________________________
0 + 0 + ab + 0 + bc + ac <---- final expression
_____________________________
this tends to **ab + bc + ac.
****(iii) 2p** 2 q 2 – 3pq + 4, 5 + 7pq – 3p 2 q 2
**Solution:
As here two expressions are given, we need to place expressions same terms below other expressions same term one by one then we will get like these:
2p2q2 - 3pq + 4
+ -3p2q2 + 7pq +5
__________________
-1p2q2 + 4pq + 9 <-------- final expression
____________________
this tends to -1p 2 q 2 + 4pq + 9.
****(iv) l** 2 + m 2 , m 2 **+ n 2 , n 2 + l 2 , 2lm + 2mn + 2nl
**Solution:
As here four expressions are given, we need to place expressions same terms below other expressions same term one by one then we will get like these:
l2 + m2
+ 0 + m2 + n2
+ l2 + 0 + n2
+ 0 + 0 + 0 + 2lm + 2mn + 2nl
_________________________________
2l2 + 2m2 + 2n2 + 2lm + 2mn + 2nl <---------final expression
___________________________________
as 2 is common among all terms then we can take it common this tends to **2( l 2 **+ m 2 **+ n 2 **+ lm + mn + nl)
**Question 4.
****(a) Subtract 4a – 7ab + 3b + 12 from 12a – 9ab + 5b – 3**
**Solution:
Here we need to subtract the given expressions:
then,
12a – 9ab + 5b – 3
(-) 4a – 7ab + 3b + 12
________________________
in subtraction sign of (-) expression gets altered as:
12a – 9ab + 5b – 3
- 4a + 7ab - 3b - 12
________________________
8a - 2ab + 2b - 15 <---------final expression
__________________________
this tends to **8a - 2ab + 2b - 15 .
****(b) Subtract 3xy + 5yz – 7zx from 5xy – 2yz – 2zx + 10xyz**
**Solution:
Here we need to subtract the given expressions:
then,
5xy – 2yz – 2zx + 10xyz
(-) 3xy + 5yz – 7zx + 0
___________________________
in subtraction sign of (-) expression gets altered as:
5xy – 2yz – 2zx + 10xyz
-3xy - 5yz + 7zx - 0
___________________________
2xy - 7yz + 5zx + 10xyz <----------- final expression
_____________________________
this tends to **2xy - 7yz + 5zx + 10xyz.
****(c) Subtract 4p** 2 q – 3pq + 5pq 2 – 8p + 7q – 10 from18 – 3p – 11q + 5pq – 2pq 2 **+ 5p 2 q
**Solution:
Here we need to subtract the given expressions:
then, 5p2q + 5pq - 2pq2 - 3p - 11q + 18
(-) 4p2q – 3pq + 5pq2 – 8p + 7q – 10
__________________________________
in subtraction sign of (-) expression gets altered as:
5p2q + 5pq - 2pq2 - 3p - 11q + 18
-4p2q + 3pq - 5pq2 + 8p - 7q + 10
__________________________________
p2q + 8pq - 7pq2 + 5p - 18q + 28 <-----------final expression
_____________________________________
this tends to **p 2 q + 8pq - 7pq 2 **+ 5p - 18q + 28
Summary
Chapter 9 of NCERT Class 8 Mathematics focuses on algebraic expressions and identities. Exercise 9.1 specifically deals with the identification of monomials, binomials, and trinomials, as well as like and unlike terms. Students learn to recognize and classify different types of algebraic expressions based on the number of terms they contain. The exercise also covers the concept of coefficients and how to identify them in various terms.