Question

Evaluate the following using suitable identities: ${\left(99\right)}^3$

Answer 1

${\left(99\right)}^3$

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

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

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

= 1000000 - 1 -300(99)

= 1000000 − 1 − 29700

= 970299