Word Count : 245

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Let (F \subset K) and (\alpha, \beta \in K) be algebraic over (F) of degrees (m) and (n), respectively. That is, the minimal polynomial of (\alpha) over (F) has degree (m) and that of (\beta) over (F) has degree (n). Consider the field extension (F(\alpha, \beta)) over (F). By the tower law, [ [F(\alpha, \beta) : F] = [F(\alpha, \beta) : _______ _________ ___ ______ ______ _______ ____.
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