Evaluate the $(99)^{3}$ using suitable identities.

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Solution

We have,

${(99)}^{3}$

$= {(100 - 1)}^{3}$

We know that

${(a - b)}^{3} = a^{3} - b^{3} - 3 a b (a - b)$

Therefore,

$= {(100)}^{3} - 1^{3} - 3 \times 100 \times 1 \times (100 - 1)$

$= 1000000 - 1 - 300 (100 - 1)$

$= 1000000 - 1 - 30000 + 300$

$= 970299$

Hence, this is the answer.

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