Class 8 NCERT Solutions Chapter 9 Algebraic Expressions and Identities Exercise 9.2 (original) (raw)
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) 4p** 3 , -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); (20x 2 , 5y 2 ); (4x, 3x 2 ); (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 (20x 2 ,5y 2 ):
20x2 * 5y2 = 100x2y2
**For (4x,3x 2 ):
4x * 3x2 = 12x3
**For (3mn, 4np):
3mn * 4np = 12mn2p
**Question 3. Complete the table of products.
**Ans:
| **First monomial **Second monomial | 2x | -5y | 3x2 | -4xy | 7x2y | -9x2y2 |
|---|---|---|---|---|---|---|
| 2x | 4x2 | -10xy | 6x3 | -8x2y | 14x3y | -18x3y2 |
| -5y | -10xy | 25y2 | -15x2y | 20xy2 | -35x2y2 | 45x2y3 |
| 3x2 | 6x3 | -15x2y | 9x4 | -12x3y | 21x4y | -27x4y2 |
| -4xy | -8x2y | 20xy2 | -12x3y | 16x2y2 | -28x3y2 | 36x3y3 |
| 7x2y | 14x3y | -35x2y2 | 21x4y | -28x3y2 | 49x4y2 | -63x4y3 |
| -9x2y2 | -18x3y2 | 45x2y3 | -27x4y2 | 36x3y3 | 63x4y3 | 81x4y4 |
**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, 3a 2 , 7a 4
**Ans:
5a * 3a2 * 7a4 = 105a7
****(ii) 2p , 4q , 8r**
**Ans:
2p * 4q * 8r = 64pqr
****(iii) xy, 2x** 2 y, 2xy 2
**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, -a** 2 , a 3
**Ans:
a * -a2 * a3 = -a6
****(iii) 2, 4y, 8y** 2 , 16y 3
**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.