Question

Without actually calculating the cubes, find the value of the following:
$(30{)}^3+(20{)}^3+(-50{)}^3$

Answer 1

$(30{)}^3+(20{)}^3+(-50{)}^3$
We know that $a^3+b^3+c^3=3abc,$ if $a+b+c=0$
Here $30+20-50=0$ i.e. $a+b+c=0$
$\Rightarrow (30{)}^3+(20{)}^3+(-50{)}^3$
$=3\times \left(30\right)\times \left(20\right)\times (-50)$
$=-90000$