Use the binomial theorem to find $999^{3}$ .

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Solution

$999^{3} = (1000 - 1)^{3}$

$= 1000^{3} -^{3} C_{1} \times 1000^{2} +^{3} C_{2} \times 1000 -^{3} C_{3}$

$= {(10^{3})}^{3} - 3 {(10^{3})}^{2} + 3 (10^{3}) - 1$

$= 10^{9} - 3 \times (10^{6}) + 3 \times 10^{3} - 1$

$= 1000000000 - 3 \times 1000000 + 3 \times 1000 - 1$

$= 997002999$

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