A) \[144{{a}^{2}}{{b}^{3}}{{(a+b)}^{2}}(a-b)({{a}^{2}}+ab+{{b}^{2}})\]
B) \[72{{a}^{2}}{{b}^{3}}{{(a+b)}^{2}}(a+b)({{a}^{2}}+ab+{{b}^{2}})\]
C) \[72{{a}^{2}}{{b}^{3}}{{(a+b)}^{2}}(a-b)({{a}^{2}}+ab+{{b}^{2}})\]
D) \[144{{a}^{2}}{{b}^{3}}{{(a+b)}^{2}}(a+b)({{a}^{2}}+ab+{{b}^{2}})\]
Correct Answer: C
Solution :
\[8b\left( {{a}^{2}}-{{b}^{2}} \right)=2\times 2\times 2\times b\times \left( a+b \right)\left( a-b \right)\] \[6a{{b}^{3}}\left( {{a}^{3}}-{{b}^{3}} \right)=2\times 3\times a\times b\times b\times b\] \[\left( a-b \right)\left( {{a}^{2}}+ab+{{b}^{2}} \right)\] \[18{{a}^{2}}{{(a+b)}^{2}}=2\times 3\times 3\times a\times a(a+b)\left( a+b \right)\] LCM = \[72\times {{a}^{3}}{{b}^{3}}{{\left( a+b \right)}^{2}}\left( a-b \right)\] \[\left( {{\mathbf{a}}^{\mathbf{2}}}\mathbf{+ab+}{{\mathbf{b}}^{\mathbf{2}}} \right)\]
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