Question

Evaluate: $(99{)}^3$

Answer 1

We know that,

$(a+b{)}^3=a^3+b^3+3b(a+b)$
we get,

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

By using the formula,

$={100}^3-1^3+3\left(100\right)\left(1\right)(100-1)$

$=1000000-1-300\left(99\right)$
On further calculation,

$=1000000-1-29700$

$=970299$

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