Question

Evaluate each of the following using suitable identities :

1) ${\left(103\right)}^3$

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

Answer 1

$(103{)}^3=(100+3{)}^3=(100{)}^3+3^3+3\times 100\times 3(100+3)$

$=1000000+27+90000+2700$ =$1092727$

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

$=1000000-1-30000+300$ =$970299$