Answer
$$2\sqrt{8}(3\sqrt{2}-2)=24-8\sqrt{2}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}2\sqrt{8}(3\sqrt{2}-2)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}4\sqrt{2}(3\sqrt{2}-2) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}24-8\sqrt{2}\end{aligned} $$ | |
| ① | $$ 2 \sqrt{8} =
2 \sqrt{ 2 ^2 \cdot 2 } =
2 \sqrt{ 2 ^2 } \, \sqrt{ 2 } =
2 \cdot 2 \sqrt{ 2 } =
4 \sqrt{ 2 } $$ |
| ② | $$ \color{blue}{ 4 \sqrt{2} } \cdot \left( 3 \sqrt{2}-2\right) = \color{blue}{ 4 \sqrt{2}} \cdot 3 \sqrt{2}+\color{blue}{ 4 \sqrt{2}} \cdot-2 = \\ = 24- 8 \sqrt{2} $$ |
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