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