Question
Answer
$$(-1-3\sqrt{12})\cdot(2+2\sqrt{3})=-38-14\sqrt{3}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(-1-3\sqrt{12})\cdot(2+2\sqrt{3})& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(-1-6\sqrt{3})\cdot(2+2\sqrt{3}) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}-2-2\sqrt{3}-12\sqrt{3}-36 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}-38-14\sqrt{3}\end{aligned} $$ | |
| ① | $$ - 3 \sqrt{12} =
-3 \sqrt{ 2 ^2 \cdot 3 } =
-3 \sqrt{ 2 ^2 } \, \sqrt{ 3 } =
-3 \cdot 2 \sqrt{ 3 } =
-6 \sqrt{ 3 } $$ |
| ② | $$ \color{blue}{ \left( -1- 6 \sqrt{3}\right) } \cdot \left( 2 + 2 \sqrt{3}\right) = \color{blue}{-1} \cdot2\color{blue}{-1} \cdot 2 \sqrt{3}\color{blue}{- 6 \sqrt{3}} \cdot2\color{blue}{- 6 \sqrt{3}} \cdot 2 \sqrt{3} = \\ = -2- 2 \sqrt{3}- 12 \sqrt{3}-36 $$ |
| ③ | Combine like terms |
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