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$9 - 5 \sqrt{ 6 }$
Calculate the value
$\left ( \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 6 } } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \right ) \left ( \sqrt{ \color{#FF6800}{ 6 } } \color{#FF6800}{ - } \color{#FF6800}{ 3 } \right )$
$ $ Expand using $ \left(a + b\right)\left(c + d\right) = ac + ad + bc + bd$
$\left ( \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 6 } } \right ) \sqrt{ \color{#FF6800}{ 6 } } \color{#FF6800}{ + } \left ( \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 6 } } \right ) \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 3 } \right ) \color{#FF6800}{ + } \color{#FF6800}{ 1 } \sqrt{ \color{#FF6800}{ 6 } } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 3 } \right )$
$\left ( \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 6 } } \right ) \sqrt{ \color{#FF6800}{ 6 } } + \left ( 2 \sqrt{ 6 } \right ) \times \left ( - 3 \right ) + 1 \sqrt{ 6 } + 1 \times \left ( - 3 \right )$
$ $ Get rid of unnecessary parentheses $ $
$\color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 6 } } \sqrt{ \color{#FF6800}{ 6 } } + \left ( 2 \sqrt{ 6 } \right ) \times \left ( - 3 \right ) + 1 \sqrt{ 6 } + 1 \times \left ( - 3 \right )$
$\color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 6 } } \sqrt{ \color{#FF6800}{ 6 } } + \left ( 2 \sqrt{ 6 } \right ) \times \left ( - 3 \right ) + 1 \sqrt{ 6 } + 1 \times \left ( - 3 \right )$
$ $ Simplify the expression $ $
$\color{#FF6800}{ 12 } + \left ( 2 \sqrt{ 6 } \right ) \times \left ( - 3 \right ) + 1 \sqrt{ 6 } + 1 \times \left ( - 3 \right )$
$12 + \left ( \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 6 } } \right ) \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 3 } \right ) + 1 \sqrt{ 6 } + 1 \times \left ( - 3 \right )$
$ $ Get rid of unnecessary parentheses $ $
$12 \color{#FF6800}{ - } \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 6 } } \color{#FF6800}{ \times } \color{#FF6800}{ 3 } + 1 \sqrt{ 6 } + 1 \times \left ( - 3 \right )$
$12 \color{#FF6800}{ - } \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 6 } } \color{#FF6800}{ \times } \color{#FF6800}{ 3 } + 1 \sqrt{ 6 } + 1 \times \left ( - 3 \right )$
$ $ Simplify the expression $ $
$12 \color{#FF6800}{ - } \color{#FF6800}{ 6 } \sqrt{ \color{#FF6800}{ 6 } } + 1 \sqrt{ 6 } + 1 \times \left ( - 3 \right )$
$12 - 6 \sqrt{ 6 } + \color{#FF6800}{ 1 } \sqrt{ 6 } + 1 \times \left ( - 3 \right )$
$ $ Multiplying any number by 1 does not change the value $ $
$12 - 6 \sqrt{ 6 } + \sqrt{ 6 } + 1 \times \left ( - 3 \right )$
$12 - 6 \sqrt{ 6 } + \sqrt{ 6 } + \color{#FF6800}{ 1 } \times \left ( - 3 \right )$
$ $ Multiplying any number by 1 does not change the value $ $
$12 - 6 \sqrt{ 6 } + \sqrt{ 6 } \color{#FF6800}{ - } \color{#FF6800}{ 3 }$
$\color{#FF6800}{ 12 } - 6 \sqrt{ 6 } + \sqrt{ 6 } \color{#FF6800}{ - } \color{#FF6800}{ 3 }$
$ $ Subtract $ 3 $ from $ 12$
$\color{#FF6800}{ 9 } - 6 \sqrt{ 6 } + \sqrt{ 6 }$
$9 \color{#FF6800}{ - } \color{#FF6800}{ 6 } \sqrt{ \color{#FF6800}{ 6 } } \color{#FF6800}{ + } \sqrt{ \color{#FF6800}{ 6 } }$
$ $ Calculate between similar terms $ $
$9 \color{#FF6800}{ - } \color{#FF6800}{ 5 } \sqrt{ \color{#FF6800}{ 6 } }$
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