Question

Using a suitable algebraic identity, the value of ${101}^3$ is ___ .

Answer 1

Using algebraic identity $(a+b{)}^3=(a^3+b^3+3a^{2}b+3a{b}^2)$

$101=(100+1{)}^3=(100{)}^3+(1{)}^3+3\times {100}^2\times 1+3\times 100\times 1^2$

$=1000000+1+30000+300$

$=1030301$