Question

Evaluate using algebraic formula:

10.1³

Answer 1

10.1³ = (10 + 0.1)³

Let a = 10, b = 0.1

Using the identity,

(a ± b)³ = a³ ± 3a²b + 3ab² ± b³

(10 + 0.1)³ = (10)³ + 3(10)²(0.1) + 3(10)(0.1)² + (0.1)³

= 1000 + 3(100)(0.1) + 3(10)(0.01) + 0.001

= 1000 + 3(10) + 3(0.1) + 0.001

= 1000 + 30 + 0.3 + 0.001

= 1030 + 0.301

∴ (10 + 0.1)³ = 1030.301

Hence, 10.1³ = 1030.301