Evaluate each of the following:$104^3 + 96^3$

Given:

$104^3 + 96^3$

To do:

We have to evaluate $104^3 + 96^3$.

Solution:

We know that,

$(a+b)^3=a^3 + b^3 + 3ab(a+b)$

$(a-b)^3= a^3-b^3-3ab(a-b)$

This implies,

$(a + b)^3 + (a- b)^3 = 2(a^3 + 3ab^2)$

$(a + b)^3 - (a - b)^3 = 2(b^3 + 3a^2b)$

Therefore,

$104^3 + 96^3 = (100 + 4)^3 + (100 - 4)^3$

$= 2[(100)^3 + 3 \times 100 \times (4)^2]$

$= 2[ 1000000 + 300 \times 16]$

$= 2[ 1000000 + 4800]$

$= 1004800 \times 2$

$= 2009600$

Hence, $104^3 + 96^3 = 2009600$.

Tutorialspoint

Updated on: 10-Oct-2022

30 Views

Kickstart Your Career

Get certified by completing the course

Get Started