A) \[{{a}^{2}}{{b}^{2}}\,\,({{a}^{2}}-{{b}^{2}})\]
B) \[ab\,\,({{a}^{2}}-{{b}^{2}})\]
C) \[{{a}^{2}}{{b}^{2}}+a{{b}^{3}}\]
D) \[{{a}^{3}}{{b}^{3}}\,\,({{a}^{2}}-{{b}^{2}})\]
Correct Answer: A
Solution :
Here, \[{{a}^{3}}b-a{{b}^{3}}=ab\,\,({{a}^{2}}-{{b}^{2}})=ab\,\,(a-b)(a+b)\] \[{{a}^{3}}{{b}^{2}}+{{a}^{2}}{{b}^{3}}={{a}^{2}}{{b}^{2}}\,\,(a+b)\] and \[ab\,\,(a+b)=ab\,\,(a+b)\] \[\therefore \] \[LCM\,\,[({{a}^{3}}b-a{{b}^{3}}),({{a}^{3}}{{b}^{2}}+{{a}^{2}}{{b}^{3}}),ab\,\,(a+b)]\] \[={{a}^{2}}{{b}^{2}}(a+b)(a-b)={{a}^{2}}{{b}^{2}}({{a}^{2}}-{{b}^{2}})\]
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