what is the following product?\n$(2\\sqrt{7}+3\\sqrt{6})(5\\sqrt{2}+4\\sqrt{3})$\n$6\\sqrt{10}+16\\sqrt{2}+42…

what is the following product?\n$(2\\sqrt{7}+3\\sqrt{6})(5\\sqrt{2}+4\\sqrt{3})$\n$6\\sqrt{10}+16\\sqrt{2}+42$\n$8\\sqrt{10}+30\\sqrt{2}+66$\n$7\\sqrt{14}+6\\sqrt{21}+16\\sqrt{3}+21\\sqrt{2}$\n$10\\sqrt{14}+8\\sqrt{21}+30\\sqrt{3}+36\\sqrt{2}$

what is the following product?\n$(2\\sqrt{7}+3\\sqrt{6})(5\\sqrt{2}+4\\sqrt{3})$\n$6\\sqrt{10}+16\\sqrt{2}+42$\n$8\\sqrt{10}+30\\sqrt{2}+66$\n$7\\sqrt{14}+6\\sqrt{21}+16\\sqrt{3}+21\\sqrt{2}$\n$10\\sqrt{14}+8\\sqrt{21}+30\\sqrt{3}+36\\sqrt{2}$

Answer

Explanation:

Step1: Use FOIL method

$(2\sqrt{7}+3\sqrt{6})(5\sqrt{2}+4\sqrt{3})=2\sqrt{7}\times5\sqrt{2}+2\sqrt{7}\times4\sqrt{3}+3\sqrt{6}\times5\sqrt{2}+3\sqrt{6}\times4\sqrt{3}$

Step2: Simplify each term

$2\sqrt{7}\times5\sqrt{2}=10\sqrt{14}$; $2\sqrt{7}\times4\sqrt{3}=8\sqrt{21}$; $3\sqrt{6}\times5\sqrt{2}=3\times5\sqrt{12}=15\times2\sqrt{3}=30\sqrt{3}$; $3\sqrt{6}\times4\sqrt{3}=3\times4\sqrt{18}=12\times3\sqrt{2}=36\sqrt{2}$

Step3: Combine terms

$10\sqrt{14}+8\sqrt{21}+30\sqrt{3}+36\sqrt{2}$

Answer:

$10\sqrt{14}+8\sqrt{21}+30\sqrt{3}+36\sqrt{2}$