## Chapter 5 Expansion Formulae Set 5.2

Question 1.

Expand:

i. (k + 4)Â³

ii. (7x + 8y)Â³

iii. (7x + m)Â³

iv. (52)Â³

v. (101)Â³

Solution:

i. Here, a = k and b = 4

(k + 4)Â³ = (k)Â³ + 3(k)Â² (4) + 3(k)(4)Â² + (4)Â³

â€¦[âˆµ (a + b)Â³ = aÂ³ + 3aÂ²b + 3abÂ² + bÂ³]

= kÂ³ + 12kÂ² + 3(k)(16) + 64

= kÂ³ + 12kÂ² + 48k + 64

ii. Here, a = 7x and b = 8y

(7x + 8y)Â³

= (7x)Â³ + 3(7x)Â² (8y) + 3(7x) (8y)Â² + (8y)Â³

â€¦[âˆµ (a + b)Â³ = aÂ³ + 3aÂ²b + 3abÂ² + bÂ³]

= 343xÂ³ + 3(49xÂ²)(8y) + 3(7x)(64yÂ²) + 512yÂ³

= 343xÂ³ + 1176xÂ²y + 1344xyÂ² + 512yÂ³

iii. Here, a = 7 and b = m

(7 + m)Â³ = (7)Â³ + 3(7)Â²(m) + 3(7)(m)Â² + (m)Â³

â€¦[âˆµ (a + b)Â³ = aÂ³ + 3aÂ²b + 3abÂ² + bÂ³]

= 343 + 3(49)(m) + 3(7)(mÂ²) + mÂ³

= 343 + 147m + 21mÂ² + mÂ³

iv. (52)Â³ = (50 + 3)Â³

Here, a = 50 and b = 2

(52)Â³ = (50)Â³ + 3(50)Â² (2) + 3(50)(2)Â² + (2)Â³

â€¦[âˆµ (a + b)Â³ = aÂ³ + 3aÂ²b + 3abÂ² + bÂ³]

= 125000 + 3(2500)(2) + 3(50)(4) + 8

= 125000 + 15000 + 600 + 8

=140608

v. (101)Â³ = (100 + 1)Â³

Here, a = 100 and b = 1

(101)Â³

= (100)Â³ + 3(100)Â²(1) + 3(100)(1)Â² + (1)Â³

â€¦[âˆµ (a + b)Â³ = aÂ³ + 3aÂ²b + 3abÂ² + bÂ³]

= 1000000 + 3(10000) + 3(100) (1) + 1

= 1000000 + 30000 + 300 + 1

= 1030301

vi. Here, a = x and b = 1/x

vii. Here, a = 2m and b = 1/5

viii. Here, a = 5x/v and b = y/5x