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

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:  

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.