Find the value of the expression given below, correct up to 2 decimal places.…

Concept

For any numbers a and b, the difference-of-cubes identity is a3 − b3 = (a − b)(a2 + ab + b2).

Therefore, when a2 + ab + b2 is nonzero, (a3 − b3)/(a2 + ab + b2) simplifies to a − b.

Application

1. Let a = 0.96 and b = 0.10.

2. The denominator is a2 + ab + b2 = 0.9216 + 0.096 + 0.01 = 1.0276, so it is nonzero.

3. Using the identity, the expression becomes a − b = 0.96 − 0.10 = 0.86.

Cross-check

Directly, the numerator is 0.963 − 0.103 = 0.884736 − 0.001 = 0.883736.

Also, 1.0276 × 0.86 = 0.883736, which reproduces the numerator. Hence the quotient is 0.86, already correct to two decimal places.