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:  

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, 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

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