## 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 Ã— 7p = (4 Ã— 7) Ã— p = 28p

(ii) -4p Ã— 7p = (-4 Ã— 7) Ã— p Ã— p = -28p^{2}

(iii) -4p Ã— 7pq = (-4 Ã— 7) Ã— p Ã— pq = -28p^{2}q

(iv) 4p^{3} Ã— -3p = (4 Ã— -3) Ã— p^{3} Ã— p = -12p^{4}

(v) 4p x 0 = (4 Ã— 0) Ã— p = 0 Ã— p = 0

Ex 9.2 Class 8 MathsÂ 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 Ã— breadth = p Ã— q = pq sq units

(ii) Length = 10 m units, breadth = 5n units

Area of the rectangle = length Ã— breadth = 10 m Ã— 5 n = (10 Ã— 5) Ã— m Ã— n = 50 mn sq units

(iii) Length = 20x^{2} units, breadth = 5y^{2} units

Area of the rectangle = length Ã— breadth = 20x^{2} Ã— 5y^{2} = (20 Ã— 5) Ã— x^{2} Ã— y^{2} = 100x^{2}y^{2} sq units

(iv) Length = 4x units, breadth = 3x^{2} units

Area of the rectangle = length Ã— breadth = 4x Ã— 3x^{2} = (4 Ã— 3) Ã— x Ã— x^{2} = 12x^{3} sq units

(v) Length = 3mn units, breadth = 4np units

Area of the rectangle = length Ã— breadth = 3mn Ã— 4np = (3 Ã— 4) Ã— mn Ã— np = 12mn^{2}p sq units

Ex 9.2 Class 8 MathsÂ Question 3.

Complete the table of Products.

Solution:

Completed Table

Ex 9.2 Class 8 MathsÂ 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 Ã— b Ã— h = 5a Ã— 3a^{2} Ã— 7a^{4} = 105 a^{7} cu. units

(ii) Here, length = 2p, breadth = 4q, height = 8r

Volume of the box = l Ã— b Ã— h = 2p Ã— 4q Ã— 8r = 64pqr cu. units

(iii) Here, length = xy, breadth = 2x^{2}y, height = 2xy^{2}

Volume of the box = l Ã— b Ã— h = xy Ã— 2x^{2}y Ã— 2xy^{2} = (1 Ã— 2 Ã— 2) Ã— xy Ã— x^{2}y Ã— xy^{2} = 4x^{4}y^{4} cu. units

(iv) Here, length = a, breadth = 2b, height = 3c

Volume of the box = length Ã— breadth Ã— height = a Ã— 2b Ã— 3c = (1 Ã— 2 Ã— 3)abc = 6 abc cu. units

Ex 9.2 Class 8 MathsÂ 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 Ã— yz Ã— zx = x^{2}y^{2}z^{2}

(ii) a Ã— (-a^{2}) Ã— a^{3} = -a^{6}

(iii) 2 Ã— 4y Ã— 8y^{2} Ã— 16y^{3} = (2 Ã— 4 Ã— 8 Ã— 16) Ã— y Ã— y^{2} Ã— y^{3} = 1024y^{6}

(iv) a Ã— 2b Ã— 3c Ã— 6abc = (1 Ã— 2 Ã— 3 Ã— 6) Ã— a Ã— b Ã— c Ã— abc = 36 a^{2}b^{2}c^{2}

(v) m Ã— (-mn) Ã— mnp = [1 Ã— (-1) Ã— 1 ]m Ã— mn Ã— mnp = -m^{3}n^{2}p

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