Question

Evaluate using algebraic formula:

102³

Answer 1

102³ = (100 + 2)³

Let a = 100, b = 2

Using the identity,

(a ± b)³ = a³ ± 3a²b + 3ab² ± b³

(100 + 2)³ = (100)³ + 3(100)²(2) + 3(100)(2)² + (2)³

= 10,00,000 + 3(10,000)(2) + 3(100)(4) + 8

= 10,00,000 + 3(20,000) + 3(400) + 8

= 10,00,000 + 60,000 + 1,200 + 8

= 10,60,000 + 1,208

∴ (100 + 2)³ = 10,61,208

Hence, 102³ = 10,61,208