Question
Answer
$$(\sqrt{3}+\sqrt{5}-4\sqrt{7})(\sqrt{3}-\sqrt{5}+4\sqrt{7})=-114+8\sqrt{35}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(\sqrt{3}+\sqrt{5}-4\sqrt{7})(\sqrt{3}-\sqrt{5}+4\sqrt{7})& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}3-\sqrt{15}+4\sqrt{21}+\sqrt{15}-5+4\sqrt{35}-4\sqrt{21}+4\sqrt{35}-112 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}-114+8\sqrt{35}\end{aligned} $$ | |
| ① | $$ \color{blue}{ \left( \sqrt{3} + \sqrt{5}- 4 \sqrt{7}\right) } \cdot \left( \sqrt{3}- \sqrt{5} + 4 \sqrt{7}\right) = \color{blue}{ \sqrt{3}} \cdot \sqrt{3}+\color{blue}{ \sqrt{3}} \cdot- \sqrt{5}+\color{blue}{ \sqrt{3}} \cdot 4 \sqrt{7}+\color{blue}{ \sqrt{5}} \cdot \sqrt{3}+\color{blue}{ \sqrt{5}} \cdot- \sqrt{5}+\color{blue}{ \sqrt{5}} \cdot 4 \sqrt{7}\color{blue}{- 4 \sqrt{7}} \cdot \sqrt{3}\color{blue}{- 4 \sqrt{7}} \cdot- \sqrt{5}\color{blue}{- 4 \sqrt{7}} \cdot 4 \sqrt{7} = \\ = 3- \sqrt{15} + 4 \sqrt{21} + \sqrt{15}-5 + 4 \sqrt{35}- 4 \sqrt{21} + 4 \sqrt{35}-112 $$ |
| ② | Combine like terms |
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