Question

Evaluate each of the following using suitable identities:
$(99{)}^3$

Answer 1

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

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

Here x=100 and y=1 we get

$(100-1{)}^3$

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

=$1000000-1-30000+300$

=270299