Evaluate

\[ (9.9)^3 \]

Solution:

Using identity:

\[ (a-b)^3 = a^3-b^3-3ab(a-b) \]

\[ (9.9)^3 = (10-0.1)^3 \]

\[ = (10)^3-(0.1)^3-3(10)(0.1)(10-0.1) \]

\[ = 1000-0.001-3(9.9) \]

\[ = 1000-0.001-29.7 \]

\[ = 970.299 \]

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