Discussion
Simplify the following :
(0.9 × 0.9 × 0.9 - 0.4 × 0.4 × 0.4) / (0.9 × 0.9 + 0.4 × 0.4 + 0.9 × 0.4)
Answer: C
The expression simplifies to 0.5.
With \(a = 0.9\) and \(b = 0.4\), the numerator is \(a^{3} - b^{3}\) and the denominator is \(a^{2} + b^{2} + ab\). Since \(a^{3} - b^{3} = (a - b)(a^{2} + ab + b^{2})\), the denominator cancels:
\[ \begin{aligned} \frac{a^{3} - b^{3}}{a^{2} + ab + b^{2}} &= a - b \\ &= 0.9 - 0.4 = 0.5 \end{aligned} \]
1.3 is a + b, which would come from the sum-of-cubes identity used by mistake. 0.9 and 0.4 are just the two numbers themselves.
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