A) \[{{a}^{3}}+{{b}^{3}}\]
B) \[3({{a}^{3}}+{{b}^{3}})\]
C) \[3({{a}^{2}}+{{b}^{2}})\]
D) None of these
Correct Answer: B
Solution :
We have \[{{x}^{3}}+{{y}^{3}}+{{z}^{3}}={{(a+b)}^{3}}+{{(a\omega +b{{\omega }^{2}})}^{3}}+{{(a{{\omega }^{2}}+b\omega )}^{3}}\] \[=3{{a}^{3}}+3{{b}^{3}}+3({{a}^{2}}b+a{{b}^{2}})(1+{{\omega }^{2}}{{\omega }^{2}}+\omega {{\omega }^{4}})\] \[=3{{a}^{3}}+3{{b}^{3}}+3({{a}^{2}}b+a{{b}^{2}})(1+\omega +{{\omega }^{2}})\] \[=\]\[3({{a}^{3}}+{{b}^{3}})\] Trick: As in the previous question \[{{x}^{3}}+{{y}^{3}}+{{z}^{3}}={{(4)}^{3}}+{{(-2)}^{3}}+{{(-2)}^{3}}=48\]and (b) i.e. \[3({{a}^{3}}+{{b}^{3}})=48\]
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