Question:
Evaluate
(i) $(103)^{3}$
(ii) $(99)^{3}$
Solution:
(i) $(103)^{3}=(100+3)^{3}$
$=(100)^{3}+(3)^{3}+3(100)^{2}(3)+3(100)(3)^{2}$
$=1000000+27+90000+2700$
$=1092727$
(ii) $(99)^{3}=(100-1)^{3}$
$=(100)^{3}-(1)^{3}-3(100)^{2}(1)+3(100)(1)^{2}$
$=1000000-1-30000+300$
$=1000300-30001$
$=970299$
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