A) \[{{a}^{6}}+{{b}^{6}}\]
B) \[{{a}^{6}}-{{b}^{6}}\]
C) \[{{a}^{3}}-{{b}^{3}}\]
D) \[{{a}^{3}}+{{b}^{3}}\]
Correct Answer: B
Solution :
We have, \[(a+b)(a-b)({{a}^{2}}-ab+{{b}^{2}})({{a}^{2}}+ab+{{b}^{2}})\] \[=(a+b)({{a}^{2}}-ab+{{b}^{2}})(a-b)({{a}^{2}}+ab+{{b}^{2}})\] \[=({{a}^{3}}+{{b}^{3}})({{a}^{3}}-{{b}^{3}})={{({{a}^{3}})}^{2}}-{{({{b}^{3}})}^{2}}={{a}^{6}}-{{b}^{6}}\]
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