A) \[-\frac{{{x}^{2}}{{y}^{2}}}{40}\]
B) \[-\frac{{{x}^{2}}{{y}^{2}}}{50}\]
C) \[\frac{xy}{50}\]
D) \[-\frac{{{x}^{2}}{{y}^{2}}}{5}\]
Correct Answer: B
Solution :
\[{{\left[ 2{{x}^{2}}-\frac{1}{400}{{y}^{2}} \right]}^{2}}-{{\left[ 2{{x}^{2}}+\frac{1}{400}{{y}^{2}} \right]}^{2}}\] \[=\left[ 2{{x}^{2}}-\frac{1}{400}{{y}^{2}}+2{{x}^{2}}+\frac{1}{400}{{y}^{2}} \right]\] \[\times \left[ 2{{x}^{2}}-\frac{1}{400}{{y}^{2}}-2{{x}^{2}}-\frac{1}{400}{{y}^{2}} \right]\] \[=[4{{x}^{2}}]\left[ -\frac{2}{400}{{y}^{2}} \right]=\frac{-8{{x}^{2}}{{y}^{2}}}{400}=\frac{{{x}^{2}}{{y}^{2}}}{50}\]
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