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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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