Answer:
The product results in: [tex]6\,\sqrt{2} -2\,\sqrt{30} +6-2\,\sqrt{15}[/tex], which agrees with answer A of the given choices.
Step-by-step explanation:
We need to apply distributive property for the product of two expressions each consisting of two terms, and also use the properties of products of radicals of the same root:
[tex](\sqrt{12} +\sqrt{6} )(\sqrt{6} -\sqrt{10} )=\\=\sqrt{12*6} -\sqrt{12*10} +\sqrt{6*6} -\sqrt{6*10} =\\=\sqrt{72} -\sqrt{120} +\sqrt{36} -\sqrt{60}[/tex]
and now, we extract as many factors we can from the roots to reduce them:
[tex]\sqrt{72} -\sqrt{120} +\sqrt{36} -\sqrt{60} =\\=6\,\sqrt{2} -2\,\sqrt{30} +6-2\,\sqrt{15}[/tex]
