i. Here, a = k and b= 4
(k + 4)3 = (k)3 + 3(k)2 (4) + 3(k)(4)2 + (4)3 …[∵ (a + b)3 = a3 + 3a2b + 3ab2 + b3]
= k3 + 12k2 + 3(k)(16) + 64
= k3 + 12k2 + 48k + 64
ii. Here, a = 7x and b = 8y
(7x + 8y)3 = (7x)3 + 3(7x)2 (8y) + 3(7x) (8y)2 + (8y)3 …[∵ (a + b)3 = a3 + 3a2b + 3ab2 + b3]
= 343x3 + 3(49x2)(8y) + 3(7x)(64y2) + 512y3
= 343x3 + 1176x2y + 1344xy2 + 512y3
iii. Here, a = 7 and b = m
(7 + m)3 = (7)3 + 3(7)2(m) + 3(7)(m)2 + (m)3 …[∵ (a + b)3 = a3 + 3a2b + 3ab2 + b3]
= 343 + 3(49)(m) + 3(7)(m2) + m3
= 343 + 147m + 21m2 + m3
iv. (52)3 = (50 + 3)3
Here, a = 50 and b = 2
(52)3 = (50)3 + 3(50)2 (2) + 3(50)(2)2 + (2)3 …[∵ (a + b)3 = a3 + 3a2b + 3ab2 + b3]
= 125000 + 3(2500)(2) + 3(50)(4) + 8
= 125000 + 15000 + 600 + 8 = 140608
v. (101)3 = (100 + 1)3
Here, a = 100 and b = 1
(101)3 = (100)3 + 3(100)2(1) + 3(100)(1)2 + (1)3 …[∵ (a + b)3 = a3 + 3a2b + 3ab2 + b3]
= 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/y and b = y/5x