Question
Answer
$$(-5-3\sqrt{5})\cdot(5-2\sqrt{5})=5-5\sqrt{5}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(-5-3\sqrt{5})\cdot(5-2\sqrt{5})& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}-25+10\sqrt{5}-15\sqrt{5}+30 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}5-5\sqrt{5}\end{aligned} $$ | |
| ① | $$ \color{blue}{ \left( -5- 3 \sqrt{5}\right) } \cdot \left( 5- 2 \sqrt{5}\right) = \color{blue}{-5} \cdot5\color{blue}{-5} \cdot- 2 \sqrt{5}\color{blue}{- 3 \sqrt{5}} \cdot5\color{blue}{- 3 \sqrt{5}} \cdot- 2 \sqrt{5} = \\ = -25 + 10 \sqrt{5}- 15 \sqrt{5} + 30 $$ |
| ② | Combine like terms |
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