Skip to content
Related Articles

Related Articles

Save Article
Improve Article
Save Article
Like Article

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

  • Last Updated : 01 Dec, 2020

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) 5xyz2 – 3zy

Attention reader! All those who say programming isn't for kids, just haven't met the right mentors yet. Join the  Demo Class for First Step to Coding Coursespecifically designed for students of class 8 to 12. 

The students will get to learn more about the world of programming in these free classes which will definitely help them in making a wise career choice in the future.

Solution:



  1. Here terms are 5xyz2 and -3zy
  2. Here Coefficients are 5 and -3

(ii) 1 + x + x2

Solution:

  1. Here terms are 1, x, x2
  2. Here Coefficients are 1, 1, 1

(iii) 4x2y2 – 4x2y2z2 + z2

Solution:

  1. Here terms are 4x2y2, –4x2y2z2 and z2
  2. Here Coefficients are 4, -4 and 1

(iv) 3 – pq + qr – rp

Solution:

  1. Here terms are -3, -pq, qr, -rp
  2. Here Coefficients are 3, -1, 1 and -1

(v) x/2 + y/2 – xy

Solution:



  1. Here terms are x/2, y/2 and -xy
  2. Here Coefficients are 1/2, 1/2 and -1

(vi) 0.3a – 0.6ab + 0.5b

Solution:

  1. Here terms are 0.3a, -0.6ab and 0.5b
  2. 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 + 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

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.



  1. Example: 4x and 5y are unlike terms as they both have different variables
  2. 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) 2p2q2– 3pq + 4, 5 + 7pq – 3p2q2

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 -1p2q2 + 4pq + 9.

(iv) l2+ m2, m2 + n2, n2+ l2, 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( l2 + m2 + n2 + lm + mn + nl)

Question 4. 

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

Solution:

Here we need to substract the given expressions:

then,

                                 12a – 9ab + 5b – 3

                          (-)     4a – 7ab + 3b + 12

                             ________________________

in substraction 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 substraction 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 4p2q – 3pq + 5pq2– 8p + 7q – 10 from18 – 3p – 11q + 5pq – 2pq2 + 5p2q

Solution:

Here we need to substract the given expressions:

then,           5p2q + 5pq – 2pq2 – 3p – 11q + 18         

               (-) 4p2q – 3pq + 5pq2 – 8p + 7q – 10

               __________________________________                

in substraction 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  p2q + 8pq – 7pq2 + 5p – 18q + 28




My Personal Notes arrow_drop_up
Recommended Articles
Page :