Question
$${\text{The}}\,{\text{value}}\,{\text{of}}\,\frac{{{{\left( {0.96} \right)}^3} - {{\left( {0.1} \right)}^3}}}{{{{\left( {0.96} \right)}^2} + 0.096 + {{\left( {0.1} \right)}^2}}}\,{\text{is}}:$$
Answer: Option A $$\eqalign{
& {\text{Given}}\,{\text{expression}} \cr
& = \frac{{{{\left( {0.96} \right)}^3} - {{\left( {0.1} \right)}^3}}}{{{{\left( {0.96} \right)}^2} + \left( {0.96 \times 0.1} \right) + {{\left( {0.1} \right)}^2}}} \cr
& = {\frac{{{a^3} - {b^3}}}{{{a^2} + ab + {b^2}}}} \cr
& = \frac{\left(a-b\right) \left(a^2 + ab + b^2 \right)}{\left(a^2 + ab + b^2 \right)} \cr
& = {a - b} \cr
& = {0.96 - 0.1} \cr
& = 0.86 \cr} $$
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