A) \[{{a}^{3}}+{{b}^{3}}\]
B) \[{{a}^{3}}-{{b}^{3}}\]
C) \[{{a}^{2}}+{{b}^{2}}\]
D) \[{{a}^{2}}-{{b}^{2}}\]
E) 0
Correct Answer: B
Solution :
\[(a+b)(a+b\omega )(a+b{{\omega }^{2}})\] \[=(a+b)[{{a}^{2}}+ab(\omega +{{\omega }^{2}})+{{b}^{2}}{{\omega }^{3}}]\] \[=(a+b)({{a}^{2}}-ab+{{b}^{2}})\] \[={{a}^{3}}-{{b}^{3}}\]
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