Answer
$$(7-\sqrt{3})(2+\sqrt{3})^2=37+21\sqrt{3}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(7-\sqrt{3})(2+\sqrt{3})^2& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(7-\sqrt{3})(4+2\sqrt{3}+2\sqrt{3}+3) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(7-\sqrt{3})\cdot(7+4\sqrt{3}) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}49+28\sqrt{3}-7\sqrt{3}-12 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}37+21\sqrt{3}\end{aligned} $$ | |
| ① | $$ (2+\sqrt{3})^2 = \left( 2 + \sqrt{3} \right) \cdot \left( 2 + \sqrt{3} \right) = 4 + 2 \sqrt{3} + 2 \sqrt{3} + 3 $$ |
| ② | Combine like terms |
| ③ | $$ \color{blue}{ \left( 7- \sqrt{3}\right) } \cdot \left( 7 + 4 \sqrt{3}\right) = \color{blue}{7} \cdot7+\color{blue}{7} \cdot 4 \sqrt{3}\color{blue}{- \sqrt{3}} \cdot7\color{blue}{- \sqrt{3}} \cdot 4 \sqrt{3} = \\ = 49 + 28 \sqrt{3}- 7 \sqrt{3}-12 $$ |
| ④ | Combine like terms |
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