Evaluate each of the following:$(99)^3$

Given:

$(99)^3$

To do:

We have to evaluate $(99)^3$.

Solution:

We know that,

$(a+b)^3=a^3 + b^3 + 3ab(a+b)$

$(a-b)^3= a^3-b^3-3ab(a-b)$

Therefore,

$(99)^3 = (100 - 1)^3$

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

$= 1000000 - 1 - 300 \times 99$

$= 1000000 - 1 - 29700$

$= 1000000 - 29701$

$= 970299$

Hence, $(99)^3 = 970299$.   

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Updated on: 10-Oct-2022

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