These NCERT Solutions for Class 8 Maths Chapter 9 Algebraic Expressions and Identities Ex 9.2 Questions and Answers are prepared by our highly skilled subject experts.

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

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)

= (-28) × p^{2}

= -28p^{2}

(iii) -4p × 7pq

= {(-4) × 7} × {p × (pq)}

= -28 × (p × p × q)

= -28p^{2}q

(iv) 4p^{3} × -3p

= {4 × (-3)} × (p^{3} × p)

= -12 × (p^{4})

= -12p^{4}

(v) 4p × 0

= (4 × 0) × p

= 0 × p

= 0

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) (p, q)

Area of the rectangle = length × breadth

= p x q

= pq

(ii) (10m, 5n)

Area of the rectangle = length × breadth

= 10m × 5n

= (10 × 5) × (m × n)

= 50 × mn

= 50mn

(iii) 20x^{2}, 5y^{2}

Area of the rectangle = length × breadth

= 20x^{2} × 5y^{2}

= (20 × 5) × (x^{2} × y^{2})

= 100 × x^{2}y^{2}

= 100x^{2}y^{2}

(iv) (4x, 3x^{2})

Area of the rectangle = length × breadth

= 4x × 3x^{2}

= (4 × 3) × (x × x^{2})

= 12 × x^{3}

= 12x^{3}

(v) (3mn, 4np)

Area of the rectangle = length × breadth

= 3mn × 4np

= (3 × 4) × (mn × np)

= 12 × m × (n × n) × p

= 12 × m × n^{2} × p

= 12mn^{2}p

Question 3.

Complete the table products.

Solution:

Question 4.

Obtain the volume of rectangular boxes with the following length, breadth and height respectively.

(i) 5a, 3a^{2}, 7a4

(ii) 2p, 4q, 8r

(iii) xy, 2x^{2}y, 2xy^{2}

(iv) a, 2b, 3c

Solution:

(i) 5a, 3a^{2}, 7a^{4}

Volume of the rectangular box = length × breadth × height

= (5a) × (3a^{2}) × (7a^{4})

= (5 × 3 × 7) × (a × a^{2} × a^{4})

= 105a^{7}

(ii) 2p, 4q, 8r

Volume of the rectangular box = Length × Breadth × Height

= 2p × 4q × 8r

= (2 × 4 × 8) × (p × q × r)

= 64pqr

(iii) xy; 2x^{2}y; 2xy^{2}

Volume of the rectangular box = length × breadth × height

= xy × 2x^{2}y × 2xy^{2}

= (1 × 2 × 2) × (x × x^{2} × x) × (y × y × y^{2})

= 4 × x^{4} × y^{4}

= 4x^{4}y^{4}

(iv) a, 2b, 3c

Volume of the rectangular box = length × breadth × height

= a × 2b × 3c

= (1 × 2 × 3) × (a × b × c)

= 6abc

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

(xy) × (yz) × (zx)

= (x × x) × (y × y) × (z × z)

= x^{2} × y^{2} × z^{2}

= x^{2}y^{2}z^{2}

(ii) a; -a^{2}; a^{3}

(a) × (-a^{2}) × (a^{3})

= -(a × a^{2} × a^{3})

= -a^{6}

(iii) 2, 4y, 8y^{2}, 16y^{3}

(2) × (4y) × (8y^{2}) × (16y^{3})

= (2 × 4 × 8 × 16) × (y × y^{2} × y^{3})

= 1024y^{6}

(iv) a, 2b, 3c, 6abc

(a) × (2b) × (3c) × (6abc)

= (2 × 3 × 6) × (a × a) × (b × b) × (c × c)

= 36 × a^{2} × b^{2} × c^{2}

= 36a^{2}b^{2}c^{2}

(v) m, -mn, mnp

(m) × (-mn) × (mnp)

= -1 × (m × m × m) × (n × n) × p

= -1 × m^{3} × n^{2} × p

= -m^{3}n^{2}p