Question

Solve : $(\sqrt{2}+1{)}^6-(\sqrt{2}-1{)}^6$

Answer 1

$(\sqrt{2}+1{)}^6-(\sqrt{2}-1{)}^6=\left[\right(\sqrt{2}+1{)}^3+(\sqrt{2}-1{)}^3]\left[\right(\sqrt{2}+1{)}^3-(\sqrt{2}-1{)}^3]=[2\sqrt{2}+6+3\sqrt{2}+1+2\sqrt{2}-6+3\sqrt{2}-1][2\sqrt{2}+6+3\sqrt{2}+1-2\sqrt{2}-6-3\sqrt{2}-1]=10\sqrt{2}\cdot 14=140\sqrt{2}$