• The value of \( \Large \frac{ \left(0.96\right)^{3} - \left(0.1\right)^{3} }{ \left(0.96\right)^{2} + \left(0.096\right) + 1 } \) is

    A) 0.86

      B) 1.06

    C) 0.95

      D) 0.97

    Correct Answer:
    A) 0.86

    Description for Correct answer

    \( \Large \frac{ \left(0.96\right)^{3} - \left(0.1\right)^{3} }{ \left(0.96\right)^{2} + 0.096 + 0.01 }\)

    \(\Large \left(0.96\right)^{3} - \left(0.1\right)^{3} \) \( \Large = \left(0.96 - 0.1\right) \left[  \left(0.96\right)^{2} + 0.96 \times 0.1 + \left(0.1\right)^{2} \right] \)

    \( \Large \left[ Because, a^{3}-b^{3}= (a-b)\left(a^{2}+ab+b^{2}\right) \right] \)

    \( \Large \frac{ \left(0.96 - 0.1\right) \left[ \left(0.96\right)^{2} + 0.096 + 0.01\right] }{ \left(0.96\right)^{2} + 0.096 + 0.01 } \)

    \( \Large 0.96 - 0.1 = 0.86 \)


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