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A lazy way of saying you don't want to bother with something. You just let someone else do the work and pretend you believe them.
'I'll take your word for it' when my friend said the pizza was good, but I knew it was just burnt bread.
'I'll take your word for it' when my mom said I could skip my math homework.
'I'll take your word for it' when my brother said the video game was worth $60, even though it had one level.