Question

Evaluate (999)^3
.........​

Answer 1

$( {999})^{3}$

$( {999})^{3} = ( {1000 - 1})^{3}$

$= ( {1000})^{3} - ({1})^{3} - 3(1000)(1)(1000 - 1)$

(Using identity VII)

$( {x - y})^{3} = {x}^{3} - {y}^{3} - 3xy(x - y) \\ = {x}^{3} - {3x}^{2}y + {3xy}^{2} - {y}^{3}$

$So, \\ = 1000000000 - 1 - 2997000$

$= 997002999$

hope it helps u....!!

Answer 2

$( {999})^{3}$

$( {999})^{3} = ( {1000 - 1})^{3}$

$= ( {1000})^{3} - ({1})^{3} - 3(1000)(1)(1000 - 1)$

(Using identity VII)

$( {x - y})^{3} = {x}^{3} - {y}^{3} - 3xy(x - y) \\ = {x}^{3} - {3x}^{2}y + {3xy}^{2} - {y}^{3}$

$So, \\ = 1000000000 - 1 - 2997000$

$= 997002999$

hope it helps u....!!