well is pretty much just their product, notice all you do is, multiply each term on one side, by the other terms, sum them up, and that's all,
[tex]\bf (2-\sqrt{2})(3+\sqrt{2})\implies 2(3+\sqrt{2})~~~+~~~[-\sqrt{2}(3+\sqrt{2})]
\\\\\\
6+2\sqrt{2}~~~+~~~[-3\sqrt{2}-(\sqrt{2})^2]\implies 6+2\sqrt{2}~~~+~~~[-3\sqrt{2}-2]
\\\\\\
6+2\sqrt{2}-3\sqrt{2}-2\implies 6-2+2\sqrt{2}-3\sqrt{2}\implies 4-\sqrt{2}[/tex]
