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Felix was asked whether the following equation is an identity:$\newline$$$\left(x^{2}+1\right)^{2}=\left(x^{2}-1\right)^{2}+(2 x)^{2}$$$\newline$He performed the following steps:$\newline$$$\left(x^{2}+1\right)^{2}$$$\newline$$\stackrel{\text { Step } 1}{\hookrightarrow}=x^{4}+x^{2}+x^{2}+1$$\newline$$\stackrel{\text { Step } 2}{\hookrightarrow}=x^{4}+2 x^{2}+1$$\newline$$\stackrel{\text { Step } 3}{\hookrightarrow}=x^{4}+2 x^{2}+1-2 x^{2}+2 x^{2}$$\newline$$\stackrel{\text { Step } 4}{\hookrightarrow}=\left(x^{4}-2 x^{2}+1\right)+4 x^{2}$$\newline$$\stackrel{\text { Step } 5}{\hookrightarrow}=\left(x^{2}-1\right)^{2}+(2 x)^{2}$$\newline$For this reason, Felix stated that the equation is a true identity.$\newline$Is Felix correct? If not, in which step did he make a mistake?$\newline$Choose $1$ answer:$\newline$(A) Felix is correct.$\newline$(B) Felix is incorrect. He made a mistake in step $1$.$\newline$(C) Felix is incorrect. He made a mistake in step $3$.$\newline$(D) Felix is incorrect. He made a mistake in step $5$.