Question

Question 7
Evaluate the following using suitable identities:
(i) $(99{)}^3$
(ii) $(102{)}^3$
(iii) $(998{)}^3$

Answer 1

$\left(i\right)\left(99{)}^3\right[Usingidentity(a-b{)}^3=a^3-b^3-3ab(a-b\left)\right]\Rightarrow (100-1{)}^3=(100{)}^3+(-1{)}^3+3(100\left)\right(-1\left)\right(100-1)=1000000-1-300(100-1)=1000000-1-30000+300=970299$

$\left(ii\right)\left(102{)}^3\right[Usingidentity(a+b{)}^3=a^3+b^3+3ab(a+b\left)\right]\Rightarrow (100+2{)}^3=(100{)}^3+2^3+3\left(100\right)\left(2\right)(100+2)=1000000+8+600(100+2)=1000000+8+60000+1200=1061208$

$\left(iii\right)\left(998{)}^3\right[Usingidentity(a-b{)}^3=a^3-b^3-3ab(a-b\left)\right]\Rightarrow (1000-2{)}^3=(1000{)}^3+(-2{)}^3+3(1000\left)\right(-2\left)\right(998)=(1000{)}^3-8-6000\left(998\right)=1000000000-8-5988000=994011992$