You need a grammar book besides your dictionary. And a good text book which shows you the differences by example:

> Er kannte **beide** Wörter.
>
> Er kannte **sowohl** das eine Wort **als auch** das andere.

*Beide* is a number word meaning *all two of them*. (Same as English *both*.) In contrary *sowohl* is a conjuction which is almost always paired with *als auch*.

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The negation is as follows:

> Er kannte **keines der beiden** Wörter.
>
> Er kannte **weder** das eine Wort **noch** das andere.