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$- 9 + 7 \sqrt{ 5 }$
Calculate the value
$\left ( \color{#FF6800}{ 2 } \color{#FF6800}{ + } \color{#FF6800}{ 3 } \sqrt{ \color{#FF6800}{ 5 } } \right ) \left ( \color{#FF6800}{ 3 } \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 5 } } \right )$
$ $ Expand using $ \left(a + b\right)\left(c + d\right) = ac + ad + bc + bd$
$\color{#FF6800}{ 2 } \color{#FF6800}{ \times } \color{#FF6800}{ 3 } \color{#FF6800}{ + } \color{#FF6800}{ 2 } \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 5 } } \right ) \color{#FF6800}{ + } \left ( \color{#FF6800}{ 3 } \sqrt{ \color{#FF6800}{ 5 } } \right ) \color{#FF6800}{ \times } \color{#FF6800}{ 3 } \color{#FF6800}{ + } \left ( \color{#FF6800}{ 3 } \sqrt{ \color{#FF6800}{ 5 } } \right ) \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 5 } } \right )$
$\color{#FF6800}{ 2 } \color{#FF6800}{ \times } \color{#FF6800}{ 3 } + 2 \times \left ( - \sqrt{ 5 } \right ) + \left ( 3 \sqrt{ 5 } \right ) \times 3 + \left ( 3 \sqrt{ 5 } \right ) \times \left ( - \sqrt{ 5 } \right )$
$ $ Multiply $ 2 $ and $ 3$
$\color{#FF6800}{ 6 } + 2 \times \left ( - \sqrt{ 5 } \right ) + \left ( 3 \sqrt{ 5 } \right ) \times 3 + \left ( 3 \sqrt{ 5 } \right ) \times \left ( - \sqrt{ 5 } \right )$
$6 + \color{#FF6800}{ 2 } \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 5 } } \right ) + \left ( 3 \sqrt{ 5 } \right ) \times 3 + \left ( 3 \sqrt{ 5 } \right ) \times \left ( - \sqrt{ 5 } \right )$
$ $ Simplify the expression $ $
$6 \color{#FF6800}{ - } \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 5 } } + \left ( 3 \sqrt{ 5 } \right ) \times 3 + \left ( 3 \sqrt{ 5 } \right ) \times \left ( - \sqrt{ 5 } \right )$
$6 - 2 \sqrt{ 5 } + \left ( \color{#FF6800}{ 3 } \sqrt{ \color{#FF6800}{ 5 } } \right ) \color{#FF6800}{ \times } \color{#FF6800}{ 3 } + \left ( 3 \sqrt{ 5 } \right ) \times \left ( - \sqrt{ 5 } \right )$
$ $ Get rid of unnecessary parentheses $ $
$6 - 2 \sqrt{ 5 } + \color{#FF6800}{ 3 } \sqrt{ \color{#FF6800}{ 5 } } \color{#FF6800}{ \times } \color{#FF6800}{ 3 } + \left ( 3 \sqrt{ 5 } \right ) \times \left ( - \sqrt{ 5 } \right )$
$6 - 2 \sqrt{ 5 } + \color{#FF6800}{ 3 } \sqrt{ \color{#FF6800}{ 5 } } \color{#FF6800}{ \times } \color{#FF6800}{ 3 } + \left ( 3 \sqrt{ 5 } \right ) \times \left ( - \sqrt{ 5 } \right )$
$ $ Simplify the expression $ $
$6 - 2 \sqrt{ 5 } + \color{#FF6800}{ 9 } \sqrt{ \color{#FF6800}{ 5 } } + \left ( 3 \sqrt{ 5 } \right ) \times \left ( - \sqrt{ 5 } \right )$
$6 - 2 \sqrt{ 5 } + 9 \sqrt{ 5 } + \left ( \color{#FF6800}{ 3 } \sqrt{ \color{#FF6800}{ 5 } } \right ) \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 5 } } \right )$
$ $ Get rid of unnecessary parentheses $ $
$6 - 2 \sqrt{ 5 } + 9 \sqrt{ 5 } \color{#FF6800}{ - } \color{#FF6800}{ 3 } \sqrt{ \color{#FF6800}{ 5 } } \sqrt{ \color{#FF6800}{ 5 } }$
$6 - 2 \sqrt{ 5 } + 9 \sqrt{ 5 } \color{#FF6800}{ - } \color{#FF6800}{ 3 } \sqrt{ \color{#FF6800}{ 5 } } \sqrt{ \color{#FF6800}{ 5 } }$
$ $ Simplify the expression $ $
$6 - 2 \sqrt{ 5 } + 9 \sqrt{ 5 } \color{#FF6800}{ - } \color{#FF6800}{ 15 }$
$\color{#FF6800}{ 6 } - 2 \sqrt{ 5 } + 9 \sqrt{ 5 } \color{#FF6800}{ - } \color{#FF6800}{ 15 }$
$ $ Subtract $ 15 $ from $ 6$
$\color{#FF6800}{ - } \color{#FF6800}{ 9 } - 2 \sqrt{ 5 } + 9 \sqrt{ 5 }$
$- 9 \color{#FF6800}{ - } \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 5 } } \color{#FF6800}{ + } \color{#FF6800}{ 9 } \sqrt{ \color{#FF6800}{ 5 } }$
$ $ Calculate between similar terms $ $
$- 9 + \color{#FF6800}{ 7 } \sqrt{ \color{#FF6800}{ 5 } }$
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