Evaluate the following:

$99^3$.

Given :

The given term is $99^3$.

To do :

We have to evaluate the given term.

Solution :

$99^3$ can be written as $(100 - 1)^3$

We know that, $(a-b)^3 = a^3 - b^3 - 3ab(a-b)$

So, $(100 - 1)^3 = 100^3 - 1^3 - 3(100)(1) (100-1)$

                       $= 1000000 - 1 - 300(99)$

                      $= 1000000 - 1 - 29700$

                       $ = 999999 - 29700$

                       $ = 970299$

Therefore, the value of $99^3$ is 970299.

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Updated on: 10-Oct-2022

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