A) \[{{x}^{2}}+{{y}^{2}}\]
B) \[{{x}^{2}}-{{y}^{2}}\]
C) \[{{x}^{3}}-{{y}^{3}}\]
D) \[{{x}^{3}}+{{y}^{3}}\]
Correct Answer: C
Solution :
\[(x-y)(x\omega -y)(x{{\omega }^{2}}-y)\] \[=({{x}^{2}}\omega -xy-xy\omega +{{y}^{2}})(x{{\omega }^{2}}-y)\] \[={{x}^{3}}-{{x}^{2}}y(1+\omega +{{\omega }^{2}})+x{{y}^{2}}(1+\omega +{{\omega }^{2}})-{{y}^{3}}\] \[={{x}^{3}}-{{y}^{3}}\] \[(\because 1+\omega +{{\omega }^{2}}=0)\]You need to login to perform this action.
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