Question
Evaluate the following: $(99)^3$
✓
Answer
We know that$ (a - b)^3 = a^3 - b^3 - 3ab(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 $(99)^3 = 970299$
$\Rightarrow (99)^3$ 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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