Class 8 NCERT Solutions - Chapter 9 Algebraic Expressions and Identities - Exercise 9.2

Last Updated : 7 Aug, 2024

Question 1. Find the product of the following pairs of monomials.

Monomial: Expression containing only one term

(i) 4, 7p 

Ans: 

 (4) * (7p) = 28p

 (ii) -4p, 7p

Ans:   

(-4p) * (7p)  = -28p2

Explanation: When a negative number is multiplied to a positive number the product becomes negative.

(iii) -4p, 7pq

Ans:   

(-4p) * (7pq)  = -28p2q

(iv) 4p3, -3p

Ans:  

(4p3) * (-3p) = -12p4

(v) 4p, 0

Ans:    

(4p) * (0) = 0 

Explanation: Any number when multiplied to zero (0) gives zero.

Question 2. Find the areas of rectangles with the following pairs of monomials as their lengths and breadths respectively.

           (p, q); (10m, 5n); (20x2, 5y2); (4x, 3x2); (3mn, 4np)

Note: Area of rectangle is the product of length and breadth [length * breadth]

Ans: 

         For (p,q):

                       p * q = pq 

         For (10m, 5n):

                      10m *  5n = 50mn

         For (20x2,5y2):

                       20x2 * 5y2 = 100x2y2

         For (4x,3x2):

                         4x * 3x2 = 12x3

         For (3mn, 4np): 

                         3mn * 4np = 12mn2p

Question 3. Complete the table of products.

Ans:  

First monomial 

Second monomial  

  2x-5y3x2 -4xy7x2y-9x2y2
           2x4x2-10xy6x3-8x2y14x3y-18x3y2
          -5y-10xy25y2-15x2y20xy2-35x2y245x2y3
          3x26x3-15x2y9x4-12x3y21x4y-27x4y2
         -4xy-8x2y20xy2-12x3y16x2y2-28x3y236x3y3
          7x2y14x3y-35x2y221x4y-28x3y249x4y2-63x4y3
        -9x2y2-18x3y245x2y3-27x4y236x3y363x4y381x4y4

Question 4. Obtain the volume of rectangular boxes with the following length, breadth, and height respectively.

Note: The volume of the rectangle is the product of length, breadth, height [length * breadth * height]

(i) 5a, 3a2, 7a4

Ans: 

 5a * 3a2 * 7a4 = 105a7

(ii) 2p , 4q , 8r

Ans: 

2p * 4q * 8r = 64pqr

(iii) xy, 2x2y, 2xy2

Ans:  

xy * 2x2y * 2xy2 = 4x4y4

(iv) a, 2b, 3c

Ans:  a * 2b * 3c = 6abc

Question 5. Obtain the product of 

(i) xy, yz, zx

Ans: 

xy * yz * zx = x2y2z2

(ii) a, -a2, a3

Ans: 

a * -a2 * a3 = -a6

(iii) 2, 4y, 8y2, 16y3

Ans:

2 * 4y * 8y2 * 16y3 = 1024y6

(iv) a, 2b, 3c, 6abc

Ans: 

a * 2b * 3c * 6abc = 36a2b2c2

(v) m, -mn, mnp

Ans:

m * -mn * mnp = -m3n2p

Summary

Chapter 9, Exercise 9.2 of NCERT Class 8 Mathematics focuses on the addition and subtraction of algebraic expressions. This exercise teaches students how to combine like terms, simplify expressions by removing brackets, and perform basic operations with algebraic expressions. Students learn to apply the distributive property and identify terms that can be combined. This skill is fundamental for solving more complex algebraic problems and equations in higher mathematics.

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