Question

Evaluate the following using suitable identities: ${\left(102\right)}^3$

Answer 1

Given ${\left(102\right)}^3$​

= ${(102+2)}^3$​

Using identity ${(x+y)}^3$​= $x^3$​ + $y^3$​​ + 3xy(x + y)

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

= 1000000 + 8 + 600(102)

= 1000000 + 8 + 61200

= 1061208