If x = 332, y = 333, z = 335, then the value of x³ + y³ + z³ - 3xyz is?

Solution (By Examveda Team)

Here, x = 332, y = 333, z = 335
Find x³ + y³ + z³ - 3xyz
$$ = \frac{1}{2}\left( {x + y + z} \right)$$   $$\left[ {{{\left( {x - y} \right)}^2} + {{\left( {y - z} \right)}^2} + {{\left( {z - x} \right)}^2}} \right]$$
$$ = \left( {\frac{{332 + 333 + 335}}{2}} \right)$$   $$\left[ {{{\left( {332 - 333} \right)}^2} + {{\left( {333 - 335} \right)}^2} + {{\left( {332 - 335} \right)}^2}} \right]$$
$$\eqalign{ & = \frac{{1000}}{2}\left[ {{1^2} + {2^2} + {3^2}} \right] \cr & = \frac{{1000}}{2}\left( {14} \right) \cr & = 7000{\text{ }} \cr} $$