A) \[(a+\sqrt{2}b)({{a}^{2}}-\sqrt{2}ab+2{{b}^{2}})\]
B) \[(a-\sqrt{2}b)({{a}^{2}}+\sqrt{2}ab+2{{b}^{2}})\]
C) \[(a-\sqrt{2}b)({{a}^{2}}-\sqrt{2}ab+2{{b}^{2}})\]
D) \[(a-\sqrt{2}b)({{a}^{2}}+\sqrt{2}ab+{{b}^{2}})\]
Correct Answer: B
Solution :
(b): \[{{a}^{3}}-3\sqrt{2}{{b}^{3}}\] \[={{a}^{3}}-{{(\sqrt{2}b)}^{3}}\] Then use formula, \[{{a}^{3}}-{{b}^{3}}=\left( a-b \right)\left( {{a}^{2}}+ab+{{b}^{2}} \right).\]
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