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# 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

 A) 0.86

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

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

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

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

$$\Large 0.96 - 0.1 = 0.86$$

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