Evaluate the following: 104^3+96^3 - Vidyadip

Question

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

✓

Answer

Given,
$104^3+96^3$
the above equation can be written as $(100+4)^3+(100-4)^3$
we know that, $(a+b)^3+(a-b)^3=2\left[a^3+3 a b^2\right]$
here, $a=100, b=4$
$(100+4)^3-(100-4)^3=2\left[100^3+3(4)^2(100)\right]$
$=2[1000000+4800]$
$=2[1004800]$
$=200960$
The value of $104^3+96^3=2009600$

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