A) \[xy({{x}^{2}}-{{y}^{2}}){{(x+y)}^{2}}(x-y)\]
B) \[xy({{x}^{2}}+{{y}^{2}}){{(x-y)}^{2}}{{(x+y)}^{2}}\]
C) \[xy({{x}^{2}}+{{y}^{2}}){{(x-y)}^{2}}(x+y)\]
D) \[xy({{x}^{2}}+{{y}^{2}})(x-y)(x+y)\]
Correct Answer: B
Solution :
\[{{x}^{3}}y-x{{y}^{3}}=xy(x-y)(x+y)\] \[{{x}^{4}}-2{{x}^{2}}{{y}^{2}}+{{y}^{4}}={{({{x}^{2}}-{{y}^{2}})}^{2}}\] \[={{(x-y)}^{2}}{{(x+y)}^{2}}\] \[{{x}^{4}}-{{y}^{4}}=(x-y)(x+y)({{x}^{2}}+{{y}^{2}})\] \[\therefore \] \[L.C.M=xy{{(x-y)}^{2}}{{(x+y)}^{2}}({{x}^{2}}+{{y}^{2}})\]
You need to login to perform this action.
You will be redirected in
3 sec
