Question

Evaluate using algebraic formula:

9.7³

Answer 1

9.7³ = (10 − 0.3)³

Let a = 10, b = 0.3

Using the identity,

(a ± b)³ = a³ ± 3a²b + 3ab² ± b³

(10 − 0.3)³ = (10)³ − 3(10)²(0.3) + 3(10)(0.3)² − (0.3)³

= 1000 − 3(100) (0.3) + 3(10) (0.09) − 0.027

= 1,000 − 3(30) + 3(0.9) − 0.027

= 1,000 − 90 + 2.7 − 0.027

= 910 + 2.673

∴ (10 − 0.3)³ = 912.673

Hence, 9.7³ = 912.673