Question
Answer
$$(4+2\sqrt{5})\cdot(8-3\sqrt{5})=2+4\sqrt{5}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(4+2\sqrt{5})\cdot(8-3\sqrt{5})& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}32-12\sqrt{5}+16\sqrt{5}-30 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}2+4\sqrt{5}\end{aligned} $$ | |
| ① | $$ \color{blue}{ \left( 4 + 2 \sqrt{5}\right) } \cdot \left( 8- 3 \sqrt{5}\right) = \color{blue}{4} \cdot8+\color{blue}{4} \cdot- 3 \sqrt{5}+\color{blue}{ 2 \sqrt{5}} \cdot8+\color{blue}{ 2 \sqrt{5}} \cdot- 3 \sqrt{5} = \\ = 32- 12 \sqrt{5} + 16 \sqrt{5}-30 $$ |
| ② | Combine like terms |
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