Evaluate [(0.96)³ − (0.1)³] ÷ [(0.96)² + 0.096 + (0.1)²].

Problem restatementCompute the value of the fraction where the numerator is a³ − b³ with a = 0.96, b = 0.10, and the denominator is a² + ab + b².

Given data

• a = 0.96
• b = 0.10
• ab = 0.096

Concept/ApproachUse the identity a³ − b³ = (a − b)(a² + ab + b²). Dividing (a³ − b³) by (a² + ab + b²) simplifies to a − b.

Step-by-Step calculation[(0.96)³ − (0.10)³] ÷ [(0.96)² + (0.96)(0.10) + (0.10)²] = 0.96 − 0.10= 0.86

Verification/AlternativeDirect substitution into the identity confirms immediate cancellation of the common factor.

Common pitfallsComputing all powers numerically instead of recognizing the factorization shortcut.

Final Answer0.86