Question : What is the value of $\frac{(0.5)^{3}-(0.1)^{3}}{(0.5)^{2}+0.5\times 0.1+(0.1)^{2}}$?
Option 1: $0.1$
Option 2: $0.4$
Option 3: $0.5$
Option 4: $0.6$
Correct Answer: $0.4$
Solution :
Given: $\frac{(0.5)^{3}-(0.1)^{3}}{(0.5)^{2}+0.5\times 0.1+(0.1)^{2}}$
By using the identity: $a^3-b^3=(a-b)(a^2+ab+b^2)$, the above expression can be written as:
$\frac{(0.5-0.1)(0.5^{2}+0.5\times 0.1+0.1^{2})}{(0.5)^{2}+0.5\times 0.1+(0.1)^{2}}$
= $0.5-0.1$
= $0.4$
Hence, the correct answer is $0.4$.
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