Question

Evaluate each of the following using suitable identities.
$(103{)}^3$

Answer 1

We know that $(x+y{)}^3=x^3+y^3+3xy(x+y)$

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

Here $x=100$ and $y=3$

$(100{)}^3+(3{)}^3+3\left(100\right)\left(3\right)(100+3)$

$=1000000+27+900(100+3)$

$=1000000+27+90000+2700$

$=1092727$