NCERT Solutions for Class 8 Maths Chapter 9 Algebraic Expressions and Identities Ex 9.2

NCERT Solutions for Class 8 Maths Chapter 9 Algebraic Expressions and Identities Ex 9.2

• Class 8 Maths Algebraic Expressions and Identities Exercise 9.1
• Class 8 Maths Algebraic Expressions and Identities Exercise 9.2
• Class 8 Maths Algebraic Expressions and Identities Exercise 9.3
• Class 8 Maths Algebraic Expressions and Identities Exercise 9.4
• Class 8 Maths Algebraic Expressions and Identities Exercise 9.5
• Algebraic Expressions and Identities Class 8 Extra Questions

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

Ex 9.2 Class 8 Maths Question 1.
Find the product of the following pairs of monomials.
(i) 4, 7p
(ii) -4p, 7p
(iii) -4p, 7pq
(iv) 4p ³ , -3p
(v) 4p, 0
Solution:
(i) 4 × 7p = (4 × 7) × p = 28p
(ii) -4p × 7p = (-4 × 7) × p × p = -28p ²
(iii) -4p × 7pq = (-4 × 7) × p × pq = -28p ² q
(iv) 4p ³ × -3p = (4 × -3) × p ³ × p = -12p ⁴
(v) 4p x 0 = (4 × 0) × p = 0 × p = 0

Ex 9.2 Class 8 Maths 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)
Solution:
(i) Length = p units and breadth = q units
Area of the rectangle = length × breadth = p × q = pq sq units
(ii) Length = 10 m units, breadth = 5n units
Area of the rectangle = length × breadth = 10 m × 5 n = (10 × 5) × m × n = 50 mn sq units
(iii) Length = 20x ² units, breadth = 5y ² units
Area of the rectangle = length × breadth = 20x ² × 5y ² = (20 × 5) × x ² × y ² = 100x ² y ² sq units
(iv) Length = 4x units, breadth = 3x ² units
Area of the rectangle = length × breadth = 4x × 3x ² = (4 × 3) × x × x ² = 12x ³ sq units
(v) Length = 3mn units, breadth = 4np units
Area of the rectangle = length × breadth = 3mn × 4np = (3 × 4) × mn × np = 12mn ² p sq units

Ex 9.2 Class 8 Maths Question 3.
Complete the table of Products.

Solution:
Completed Table

Ex 9.2 Class 8 Maths Question 4.
Obtain the volume of rectangular boxes with the following length, breadth and height respectively.
(i) 5a, 3a ² , 7a ⁴
(ii) 2p, 4q, 8r
(iii) xy, 2x ² y, 2xy ²
(iv) a, 2b, 3c
Solution:
(i) Here, length = 5a, breadth = 3a ² , height = 7a ⁴
Volume of the box = l × b × h = 5a × 3a ² × 7a ⁴ = 105 a ⁷ cu. units
(ii) Here, length = 2p, breadth = 4q, height = 8r
Volume of the box = l × b × h = 2p × 4q × 8r = 64pqr cu. units
(iii) Here, length = xy, breadth = 2x ² y, height = 2xy ²
Volume of the box = l × b × h = xy × 2x ² y × 2xy ² = (1 × 2 × 2) × xy × x ² y × xy ² = 4x ⁴ y ⁴ cu. units
(iv) Here, length = a, breadth = 2b, height = 3c
Volume of the box = length × breadth × height = a × 2b × 3c = (1 × 2 × 3)abc = 6 abc cu. units

Ex 9.2 Class 8 Maths Question 5.
Obtain the product of
(i) xy, yz, zx
(ii) a, -a ² , a ³
(iii) 2, 4y, 8y ² , 16y ³
(iv) a, 2b, 3c, 6abc
(v) m, -mn, mnp
Solution:
(i) xy × yz × zx = x ² y ² z ²
(ii) a × (-a ² ) × a ³ = -a ⁶
(iii) 2 × 4y × 8y ² × 16y ³ = (2 × 4 × 8 × 16) × y × y ² × y ³ = 1024y ⁶
(iv) a × 2b × 3c × 6abc = (1 × 2 × 3 × 6) × a × b × c × abc = 36 a ² b ² c ²
(v) m × (-mn) × mnp = [1 × (-1) × 1 ]m × mn × mnp = -m ³ n ² p

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