AMC 10A 2020 Problem 14

Real numbers x and y satisfy x+y=4 and x \cdot y=-2. What is the value of

x+\dfrac{x^{3}}{y^{2}}+\dfrac{y^{3}}{x^{2}}+y ?

Answer Choices
A. 360
B. 400
C. 420
D. 440
E. 480