Question

evaluate the following. i. ( 9.9)cube. ii. (10.4)cube

Answer 1

i- 970.299
ii- 1124.864

Answer 2

1..)
$( {9.9})^{3}$
$= ({10.0 - 0.1})^{3}$
therefore
$( {x- y})^{3} = {x}^{3} - {y}^{3} - 3xy(x - y)$
$= ({10.0})^{3} - ( {0.1})^{3} - 3(10.0)(0.1)(10.0 - 0.1)$
$= 1000 - 0.001 - 3(9.9)$
$= 999.999 - 29.7$
$= 970.299$
2..)
$( {10.4})^{3}$
$= ( {10.0 + 0.4})^{3}$
therefore
$( {x + y})^{3} = {x}^{3} + {y}^{3} + 3xy(x + y)$
$= ( {10.0})^{3} + ( {0.4})^{3} + 3(10.0)(0.4 )(10.0 + 0.4)$
$= 1000 + 0.064 + 12(10.4)$
$= 1000.064 +124.8$
$= 1124.864$
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