what is the following product?\n$\\left(\\sqrt{12}+\\sqrt{6}\\right)\\left(\\sqrt{6}-\\sqrt{10}\\right)$\n$6\…

what is the following product?\n$\\left(\\sqrt{12}+\\sqrt{6}\\right)\\left(\\sqrt{6}-\\sqrt{10}\\right)$\n$6\\sqrt{2}-2\\sqrt{30}+6 - 2\\sqrt{15}$\n$6\\sqrt{3}-6\\sqrt{5}$\n$3\\sqrt{2}-\\sqrt{22}+2\\sqrt{3}-4$\n$2\\sqrt{3}+6 - 2\\sqrt{15}$

what is the following product?\n$\\left(\\sqrt{12}+\\sqrt{6}\\right)\\left(\\sqrt{6}-\\sqrt{10}\\right)$\n$6\\sqrt{2}-2\\sqrt{30}+6 - 2\\sqrt{15}$\n$6\\sqrt{3}-6\\sqrt{5}$\n$3\\sqrt{2}-\\sqrt{22}+2\\sqrt{3}-4$\n$2\\sqrt{3}+6 - 2\\sqrt{15}$

Answer

Explanation:

Step1: Use FOIL method

$(\sqrt{12}+\sqrt{6})(\sqrt{6}-\sqrt{10})=\sqrt{12}\times\sqrt{6}-\sqrt{12}\times\sqrt{10}+\sqrt{6}\times\sqrt{6}-\sqrt{6}\times\sqrt{10}$

Step2: Simplify each term

  • $\sqrt{12}\times\sqrt{6}=\sqrt{12\times6}=\sqrt{72}=6\sqrt{2}$
  • $\sqrt{12}\times\sqrt{10}=\sqrt{12\times10}=\sqrt{120}=2\sqrt{30}$
  • $\sqrt{6}\times\sqrt{6}=6$
  • $\sqrt{6}\times\sqrt{10}=\sqrt{6\times10}=\sqrt{60}=2\sqrt{15}$

Step3: Combine the terms

$6\sqrt{2}-2\sqrt{30}+6 - 2\sqrt{15}$

Answer:

$6\sqrt{2}-2\sqrt{30}+6 - 2\sqrt{15}$