A) \[{{a}^{4}}({{b}^{2}}-{{c}^{2}})+{{b}^{4}}({{c}^{2}}-{{b}^{2}})+{{c}^{4}}({{a}^{2}}-{{b}^{2}})\]
B) \[a{{(b-c)}^{3}}+b{{(c-a)}^{3}}+c{{(a-b)}^{3}}\]
C) \[{{(a+b+c)}^{3}}-{{(b+c-a)}^{3}}-{{(c+a-b)}^{3}}-{{(a+b-c)}^{3}}\]
D) \[a({{b}^{4}}-{{c}^{4}})+b({{c}^{4}}-{{a}^{4}})+c({{a}^{4}}+{{b}^{4}})\]
Correct Answer: A
Solution :
\[{{a}^{4}}({{b}^{2}}-{{c}^{2}})+{{b}^{4}}({{c}^{2}}-{{a}^{2}})+{{c}^{4}}({{a}^{2}}-{{b}^{2}})\] \[=({{a}^{4}}{{b}^{2}}-{{b}^{4}}{{a}^{2}})+({{b}^{4}}{{c}^{2}}-{{a}^{4}}{{c}^{2}})+{{c}^{4}}({{a}^{2}}-{{b}^{2}})\] \[={{a}^{2}}{{b}^{2}}({{a}^{2}}-{{b}^{2}})-{{c}^{2}}({{a}^{4}}-{{b}^{4}})+{{c}^{4}}({{a}^{2}}-{{b}^{2}})\] \[=(ab)\{{{a}^{2}}{{b}^{2}}(a-b)-{{c}^{2}}(a-b)-{{c}^{2}}\]\[(a-b)({{a}^{2}}+{{b}^{2}})+{{c}^{4}}(a-b)\}\]
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