Question

The value of $(90{)}^3-(80{)}^3-3\times 90\times 80\times 10=$___

Answer 1

We know that $(a-b{)}^3=a^3-b^3-3ab(a-b)$

$\Rightarrow (90-80{)}^3=(90{)}^3-(80{)}^3-3\times 90\times 80\times (90-80)$

$\Rightarrow (90{)}^3-(80{)}^3-3\times 90\times 80\times 10$ = $(90-80{)}^3$=${10}^3$=1000