## 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) 4p³, - 3p

v) 4p, 0

Answer:

a) 4 × 7p = 28p

b) -4p × 7p = -28p²

c) -4p × 7pq = -28p²q

d) 4p³ × -3p = -12p⁴

e) 4p × 0 = 0

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)

Answer:

Area of rectangle = l × b

= 10m × 5n

= 50mn

Area of rectangle = l × b

= 20x² × 5y²

= 100x²y²

Area of rectangle = l × b

= 4x × 3x²

= 12x³

Area of rectangle = l × b

= 3mn × 4np

= 12n²mp

Question 3: Complete the table of products.

Answer:

Question 4: Obtain the volume of rectangular boxes with the following length, breadth and height respectively.

i) 5a, 3a², 7a⁴

ii) 2p, 4q, 8r

iii) xy, 2x²y, 2xy²

iv) a, 2b, 3c

Answer:

i)

Volume of cuboid = length × width × height

= 5a × 3a² × 7a⁴

= 105a⁷

ii)

Volume of cuboid = length × width × height

= 2p × 4q × 8r

= 64pqr

iii)

Volume of cuboid = length × width × height

= xy × 2x²y × 2xy²

= 4x⁴y⁴

iv)

Volume of cuboid = length × width × height

= a × 2b × 3c

= 6abc

Question 5: Obtain the product of

i) xy, yz, zx

ii) a, - a², a³

iii) 2, 4y, 8y², 16y³

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

v) m, - mn, mnp

Answer:

i)

= xy × yz × zx

= x²y²z²

ii)

= a × (-a²) × a³

= -a⁶

iii)

= 2 × 4y × 8y² × 16y³

= 1024y⁶

iv)

= a × 2b × 3c × 6abc

= 36a²b²c²

v)

= m × (-mn) × mnp

= -m³n²p

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