$M[x_1,...,x_n]\cong M\otimes_RR[x_1,...,x_n]$

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Let $R$ be a commutative ring with 1, $M$ an $R$-module. I know $M[x]\cong M\otimes_RR[x]$. Is it true that we can extend this to the more general case, i.e., $M[x_1,...,x_n]\cong M\otimes_RR[x_1,...,x_n]$?