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Real numbers $x$ and $y$ satisfy $x^{3}+y^{3}=4$ and $xy = 2$. What is the value of $2xy+\frac{x^{4}}{y^{2}}+\frac{y^{4}}{x^{2}}$? (Adapted From 2020 AMC 10A Problem, Question \#14) 
Overseas Competition->Knowledge Point->Calculation Modules
$2xy+\frac{x^{4}}{y^{2}}+\frac{y^{4}}{x^{2}} = 2xy+\frac{x^{6}+y^{6}}{x^{2}y^{2}} = \frac{2xyx^{2}y^{2}+x^{6}+y^{6}}{x^{2}y^{2}}= \frac{2x^{3}y^{3}+x^{6}+y^{6}}{x^{2}y^{2}} $  $= \frac{(x^{3}+y^{3})^{2}}{x^{2}y^{2}} =\frac{4^{2}}{4}= 4$. 