Answer
$$(3\sqrt{3}-4\sqrt{5})(3\sqrt{3}+4\sqrt{5})=-53$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(3\sqrt{3}-4\sqrt{5})(3\sqrt{3}+4\sqrt{5})& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}27+12\sqrt{15}-12\sqrt{15}-80 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}-53\end{aligned} $$ | |
| ① | $$ \color{blue}{ \left( 3 \sqrt{3}- 4 \sqrt{5}\right) } \cdot \left( 3 \sqrt{3} + 4 \sqrt{5}\right) = \color{blue}{ 3 \sqrt{3}} \cdot 3 \sqrt{3}+\color{blue}{ 3 \sqrt{3}} \cdot 4 \sqrt{5}\color{blue}{- 4 \sqrt{5}} \cdot 3 \sqrt{3}\color{blue}{- 4 \sqrt{5}} \cdot 4 \sqrt{5} = \\ = 27 + 12 \sqrt{15}- 12 \sqrt{15}-80 $$ |
| ② | Combine like terms |
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