Question
Mathematics
1. $\left(\sqrt{6}-4\right)\left(2\sqrt{6}+8\right)$(sqrt6-4)(2sqrt6+8)
Solve problem with AI
Answer: $-20\sqrt{6}$-20sqrt6
Solution:
$\left(\sqrt{6}-4\right)\left(2\sqrt{6}+8\right)$(sqrt6-4)(2sqrt6+8)
$=\sqrt{6}\cdot 2\sqrt{6}+\sqrt{6}\cdot 8-4\cdot 2\sqrt{6}-4\cdot 8$=sqrt6*2sqrt6+sqrt6*8-4*2sqrt6-4*8 (distributive property of multiplication)
$=2\cdot 6+8\sqrt{6}-8\sqrt{6}-32$=2*6+8sqrt6-8sqrt6-32
$=12-32$=12-32
$=-20$=-20
Therefore, $\left(\sqrt{6}-4\right)\left(2\sqrt{6}+8\right)=-20$(sqrt6-4)(2sqrt6+8)=-20. But if we assume that we need a numerical answer, we can simplify it further as:
$\left(\sqrt{6}-4\right)\left(2\sqrt{6}+8\right)=-20$(sqrt6-4)(2sqrt6+8)=-20
$=-20\sqrt{6}\cdot \frac{\sqrt{6}}{\sqrt{6}}$=-20sqrt6*(sqrt6)/(sqrt6)
$=-20\sqrt{6}\cdot \frac{\sqrt{6}\cdot \sqrt{6}}{6}$=-20sqrt6*(sqrt6*sqrt6)/(6)
$=-20\sqrt{6}\cdot \frac{\sqrt{36}}{6}$=-20sqrt6*(sqrt36)/(6)
$=-20\sqrt{6}\cdot 1$=-20sqrt6*1
$=-20\sqrt{6}$=-20sqrt6
So, $\left(\sqrt{6}-4\right)\left(2\sqrt{6}+8\right)=-20\sqrt{6}$(sqrt6-4)(2sqrt6+8)=-20sqrt6.
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