Question : Simplify the given expression.
$\frac{0.24 \times 0.24 \times 0.24-0.008}{0.24 \times 0.24+0.048+0.04}$
Option 1: 0.04
Option 2: 0.02
Option 3: 0.01
Option 4: 0.03
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Correct Answer: 0.04
Solution :
$\frac{0.24\times 0.24\times 0.24-0.008}{0.24\times 0.24 + 0.048+0.04}$
= $\frac{0.24^3-0.2^3}{0.24\times 0.24 + 0.048+0.04}$
Using identity: $(a^3-b^3)=(a-b)(a^2+b^2+ab)$
= $\frac{(0.24-0.2)(0.24^2+0.24\times 0.2+0.2^2)}{0.24\times 0.24 + 0.048+0.04}$
= 0.24 – 0.2
= 0.04
Hence, the correct answer is 0.04.
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