A) \[({{x}^{2}}+{{y}^{2}})({{x}^{2}}+{{y}^{2}}-xy)\]
B) \[({{x}^{2}}+{{y}^{2}})({{x}^{2}}-{{y}^{2}})\]
C) \[({{x}^{2}}+{{y}^{2}}+xy)({{x}^{2}}+{{y}^{2}}-xy)\]
D) Factorisation is not possible
Correct Answer: C
Solution :
We have, \[{{x}^{4}}+{{y}^{4}}+{{x}^{2}}{{y}^{2}}+{{x}^{2}}{{y}^{2}}-{{x}^{2}}{{y}^{2}}\] \[={{x}^{4}}+{{y}^{4}}+2{{x}^{2}}{{y}^{2}}-{{x}^{2}}{{y}^{2}}\] \[={{({{x}^{2}}+{{y}^{2}})}^{2}}-{{(xy)}^{2}}=({{x}^{2}}+{{y}^{2}}+xy)({{x}^{2}}+{{y}^{2}}-xy)\]
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