The word that means "to spread out" is "unfurl."
Step-by-step explanation:
To "unfurl" means to unroll, spread out, or unfold something that was previously rolled up, folded, or otherwise compressed. The term can be used to describe the act of opening up a flag, a sail, or a banner, for example, or to describe the act of spreading out a sheet, a blanket, or a map. It can also be used more metaphorically to describe the act of revealing or displaying something that was previously hidden or concealed.