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A thing that swells big ends up being huge or at least really bulky.
This is a jukugo word that uses the on'yomi readings of the kanji. You should be able to read this on your own.
これからこの膨大な資料に目を通さなくてはいけないんだ。
You have to take a look at these huge documents from now on.
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Finish up whatever you are doing on the other tab(s), then close them to continue.
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