Question : Simplify the following.
$\frac{0.01 \times 0.01 \times 0.01+0.003 \times 0.003 \times 0.003}{0.05 \times 0.05 – 0.015 \times 0.05 + 0.015 \times 0.015}$
Option 1: $\frac{13}{25} \times 10^3$
Option 2: $\frac{13}{15} \times 10^{–3}$
Option 3: $\frac{13}{15} \times 10^3$
Option 4: $\frac{13}{25} \times 10^{–3}$
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Correct Answer: $\frac{13}{25} \times 10^{–3}$
Solution :
Given: $\frac{0.01 \times 0.01 \times 0.01+0.003 \times 0.003 \times 0.003}{0.05 \times 0.05–0.015 \times 0.05 + 0.015 \times 0.015}$
Converting it into the form, $a^3 + b^3 = (a + b)(a^2 - ab + b^2)$.
= $\frac{(0.01 + 0.003)((0.01)^2 – 0.01\times0.003 + (0.003)^2)}{25\times((0.01)^2 – 0.01\times0.003 +(0.003)^2)}$
= $\frac{0.013}{25}$
= $\frac{13}{25} \times 10^{–3}$
Hence, the correct answer is $\frac{13}{25} \times 10^{–3}$.
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