Question
Answer
$$\dfrac{(2\sqrt{5}-5)(2\sqrt{5}+2)}{1}=10-6\sqrt{5}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{(2\sqrt{5}-5)(2\sqrt{5}+2)}{1}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{20+4\sqrt{5}-10\sqrt{5}-10}{1} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}10-6\sqrt{5}\end{aligned} $$ | |
| ① | $$ \color{blue}{ \left( 2 \sqrt{5}-5\right) } \cdot \left( 2 \sqrt{5} + 2\right) = \color{blue}{ 2 \sqrt{5}} \cdot 2 \sqrt{5}+\color{blue}{ 2 \sqrt{5}} \cdot2\color{blue}{-5} \cdot 2 \sqrt{5}\color{blue}{-5} \cdot2 = \\ = 20 + 4 \sqrt{5}- 10 \sqrt{5}-10 $$ |
| ② | Remove 1 from denominator. |
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