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Our approach is to consider a Stanley symmetric function as a stabilized Schubert polynomial $F_{w}=\\lim_{n\\to \\infty}\\mathfrak{S}_{1^{n}\\times w}$, and study the behavior of the expansion of $\\s_{1^n\\times w}\\cdot\\s_{1^n\\times u}$ into Schubert polynomials, as $n$ increases. We prove that this expansion stabilizes and thus we get a natural expansion for the product of two Stanley symmetric functions. 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