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The binomial expansion of $\left(x^{2}+y\right)^{2}$ is $\qquad$$\newline$A. $x^{2}+2 x^{2} y+y^{2}$$\newline$B. $x^{4}+2 x^{3} y+x^{2} y^{2}$$\newline$C. $x^{4}+2 x^{2} y+y^{2}$