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She spread the newspaper out on the table.
Literal
She [topic-は] newspaper [object-を] table [possessive-の] top [on-に] spread.
広げる (ひろげる) means 'to spread out, to unfold, to open up' — it works for newspapers, maps, wings, or anything that expands from a folded or compact state. テーブルの上に ('on top of the table') uses the spatial noun 上 with に to mark the surface where the action takes place. テーブル is an English loanword that has become the standard casual word for Western-style tables.