Question

Evaluate the following:

(vi) $(99{)}^3$

Answer 1

Given, $(99{)}^3$

$=(100-1{)}^3$

Using Identity,
$(a-b{)}^3=a^3-b^3-3ab(a-b)$

$\therefore (100-1{)}^3$

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

$=1000000-1-300\left(99\right)$

$=1000000-1-29700$

$=970299$

$\therefore (99{)}^3$ =970299