Evaluate the following: (99)^3 - Vidyadip

Question

Evaluate the following:$ (99)^3$

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Answer

We know that $(a-b)^3=a^3-b^3-3 a b(a-b)$
$\Rightarrow(99)^3$ can be written as $(100-1)^3$
Here, $a =100$ and $b =1(99)^3$
$= (100 - 1)^3 = (100)^3 - (1)^3 - 3(100)(1)(100 - 1)$
$= 1000000 - 1 - (300 \times 99)$
$= 1000000 - 1 - 29700$
$= 1000000 - 29701 = 970299$
The value of $(99)^3=970299$

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