Question

Evaluate by using suitable identity : ${997}^3$

Answer 1

We have,

$(997{)}^3$

$\Rightarrow (1000-3{)}^3$

Since,

$(x-y{)}^3=x^3-y^3-3xy(x-y)$

Therefore,

$=(1000{)}^3-(3{)}^3-3\times 1000\times 3(1000-3)$

$=1000000000-27-9000\times (1000-3)$

$=1000000000-27-9000000+27000$

$=1000027000-9000027$

$=991026973$

Hence, this is the answer.