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Sydney was asked whether the following equation is an identity:$\newline$$$\left(2 x^{2}-18\right)(x+3)(x-3)=2 x^{4}-36 x^{2}+162$$$\newline$She performed the following steps:$\newline$$$\left(2 x^{2}-18\right)(x+3)(x-3)$$$\newline$$\stackrel{\text { Step } 1}{\hookrightarrow}=2\left(x^{2}-9\right)\left(x^{2}-3 x+3 x-9\right)$$\newline$$\stackrel{\text { Step } 2}{\hookrightarrow}=2\left(x^{2}-9\right)\left(x^{2}-9\right)$$\newline$$\stackrel{\text { Step } 3}{\hookrightarrow}=2\left(x^{2}-9\right)^{2}$$\newline$$\stackrel{\text { Step } 4}{\hookrightarrow}=2\left(x^{4}-18 x^{2}+81\right)$$\newline$$\stackrel{\text { Step } 5}{\hookrightarrow}=2 x^{4}-36 x^{2}+162$$\newline$For this reason, Sydney stated that the equation is a true identity.$\newline$Is Sydney correct? If not, in which step did she make a mistake?$\newline$Choose $1$ answer:$\newline$(A) Sydney is correct.$\newline$(B) Sydney is incorrect. She made a mistake in step $1$.$\newline$(C) Sydney is incorrect. She made a mistake in step $3$.$\newline$(D) Sydney is incorrect. She made a mistake in step $4$.