Answer :
Answer:
[tex]a.\quad 6\sqrt{2} - 2\sqrt{30} + 6 - 2\sqrt{15}[/tex]
Step-by-step explanation:
We are asked to find the product:
[tex]\left(\sqrt{12}\:+\:\sqrt{6}\right)\left(\sqrt{6}\:-\sqrt{10}\right)[/tex]
[tex]\mathrm{Apply\:FOIL\:method}:\:\left(a+b\right)\left(c+d\right)=ac+ad+bc+bd[/tex]
[tex]=\sqrt{12}\sqrt{6}+\sqrt{12}\left(-\sqrt{10}\right)+\sqrt{6}\sqrt{6}+\sqrt{6}\left(-\sqrt{10}\right)[/tex]
Simplify each of the individual expressions:
[tex]\sqrt{12}\sqrt{6} = \sqrt{12\cdot 6} = \sqrt{72} = \sqrt{36 \cdot 2} = \bold{6\sqrt{2}}\\\\[/tex]
[tex]\sqrt{12}\left(-\sqrt{10\right) = -\sqrt{120} = - \sqrt{4 \cdot 30} = \bold{-2\sqrt{30}}[/tex]
[tex]\sqrt{6}\sqrt{6} = \bold{6}[/tex]
[tex]\sqrt{6}\left(-\sqrt{10}\right) = -\sqrt{60} = -\sqrt{4\cdot 15} = \bold{- 2 \sqrt{15}}[/tex]
And therefore
[tex]\left(\sqrt{12}\:+\:\sqrt{6}\right)\left(\sqrt{6}\:-\sqrt{10}\right)\\\\= 6\sqrt{2} - 2\sqrt{30} + 6 - 2\sqrt{15}[/tex]
Answer:
[tex]\boxed{ 6\sqrt{2} - 2\sqrt{30} + 6 - 2\sqrt{15}}[/tex]
This corresponds to choice a.
