Question

Evaluate the following using suitable identities:
(i) $(99{)}^3$ (ii) $(102{)}^3$ (iii) $(998{)}^3$

Answer 1

(i) ${99}^3=(100-1{)}^3=(100{)}^3+(-1{)}^3-3(100\left)\right(1\left)\right(100-1)$

$=1000000-1-300(100-1)=100000-1-30000+300=970299$

(ii) ${102}^3=(100+2{)}^3=(100{)}^3+(2{)}^3+3(100\left)\right(2\left)\right(100+2)$

$=1000000+8+600(100+2)=1000000+8+60000+1200=1061208$

(iii ${998}^3=(1000-2{)}^3=(1000{)}^3-(2{)}^3-3(1000\left)\right(2\left)\right(1000-2)$

$=1000000000-8+6000(1000-2)=1000000000-8-6000000+1200=994011992$