Simplify \(\sqrt{98}\) to \(7\sqrt{2}\).
\[(5-3\sqrt{2})(1+2\sqrt{2})-7\sqrt{2}\]
Use the FOIL method: \((a+b)(c+d)=ac+ad+bc+bd\).
\[5+10\sqrt{2}-3\sqrt{2}-12-7\sqrt{2}\]
Collect like terms.
\[(5-12)+(10\sqrt{2}-3\sqrt{2}-7\sqrt{2})\]
Simplify.
\[-7\]
-7
