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Formula
Calculate the value
$\left( \sqrt{ 2 } + \sqrt{ 5 } \right) \left( 2 \sqrt{ 2 } - \sqrt{ 5 } \right)$
$- 1 + \sqrt{ 10 }$
Calculate the value
$\left ( \sqrt{ \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \sqrt{ \color{#FF6800}{ 5 } } \right ) \left ( \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 5 } } \right )$
 Expand using $\left(a + b\right)\left(c + d\right) = ac + ad + bc + bd$
$\sqrt{ \color{#FF6800}{ 2 } } \left ( \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 2 } } \right ) \color{#FF6800}{ + } \sqrt{ \color{#FF6800}{ 2 } } \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 5 } } \right ) \color{#FF6800}{ + } \sqrt{ \color{#FF6800}{ 5 } } \left ( \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 2 } } \right ) \color{#FF6800}{ + } \sqrt{ \color{#FF6800}{ 5 } } \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 5 } } \right )$
$\sqrt{ \color{#FF6800}{ 2 } } \left ( \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 2 } } \right ) + \sqrt{ 2 } \times \left ( - \sqrt{ 5 } \right ) + \sqrt{ 5 } \left ( 2 \sqrt{ 2 } \right ) + \sqrt{ 5 } \times \left ( - \sqrt{ 5 } \right )$
 Get rid of unnecessary parentheses 
$\sqrt{ \color{#FF6800}{ 2 } } \color{#FF6800}{ \times } \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 2 } } + \sqrt{ 2 } \times \left ( - \sqrt{ 5 } \right ) + \sqrt{ 5 } \left ( 2 \sqrt{ 2 } \right ) + \sqrt{ 5 } \times \left ( - \sqrt{ 5 } \right )$
$\sqrt{ \color{#FF6800}{ 2 } } \color{#FF6800}{ \times } \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 2 } } + \sqrt{ 2 } \times \left ( - \sqrt{ 5 } \right ) + \sqrt{ 5 } \left ( 2 \sqrt{ 2 } \right ) + \sqrt{ 5 } \times \left ( - \sqrt{ 5 } \right )$
 Simplify the expression 
$\color{#FF6800}{ 4 } + \sqrt{ 2 } \times \left ( - \sqrt{ 5 } \right ) + \sqrt{ 5 } \left ( 2 \sqrt{ 2 } \right ) + \sqrt{ 5 } \times \left ( - \sqrt{ 5 } \right )$
$4 + \sqrt{ 2 } \times \left ( \color{#FF6800}{ - } \sqrt{ 5 } \right ) + \sqrt{ 5 } \left ( 2 \sqrt{ 2 } \right ) + \sqrt{ 5 } \times \left ( - \sqrt{ 5 } \right )$
 Move the (-) sign forward 
$4 \color{#FF6800}{ - } \sqrt{ 2 } \sqrt{ 5 } + \sqrt{ 5 } \left ( 2 \sqrt{ 2 } \right ) + \sqrt{ 5 } \times \left ( - \sqrt{ 5 } \right )$
$4 \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 2 } } \sqrt{ \color{#FF6800}{ 5 } } + \sqrt{ 5 } \left ( 2 \sqrt{ 2 } \right ) + \sqrt{ 5 } \times \left ( - \sqrt{ 5 } \right )$
 Calculate multiplication 
$4 \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 10 } } + \sqrt{ 5 } \left ( 2 \sqrt{ 2 } \right ) + \sqrt{ 5 } \times \left ( - \sqrt{ 5 } \right )$
$4 - \sqrt{ 10 } + \sqrt{ \color{#FF6800}{ 5 } } \left ( \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 2 } } \right ) + \sqrt{ 5 } \times \left ( - \sqrt{ 5 } \right )$
 Get rid of unnecessary parentheses 
$4 - \sqrt{ 10 } + \sqrt{ \color{#FF6800}{ 5 } } \color{#FF6800}{ \times } \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 2 } } + \sqrt{ 5 } \times \left ( - \sqrt{ 5 } \right )$
$4 - \sqrt{ 10 } + \sqrt{ \color{#FF6800}{ 5 } } \color{#FF6800}{ \times } \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 2 } } + \sqrt{ 5 } \times \left ( - \sqrt{ 5 } \right )$
 Simplify the expression 
$4 - \sqrt{ 10 } + \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 10 } } + \sqrt{ 5 } \times \left ( - \sqrt{ 5 } \right )$
$4 - \sqrt{ 10 } + 2 \sqrt{ 10 } + \sqrt{ 5 } \times \left ( \color{#FF6800}{ - } \sqrt{ 5 } \right )$
 Move the (-) sign forward 
$4 - \sqrt{ 10 } + 2 \sqrt{ 10 } \color{#FF6800}{ - } \sqrt{ 5 } \sqrt{ 5 }$
$4 - \sqrt{ 10 } + 2 \sqrt{ 10 } \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 5 } } \sqrt{ 5 }$
 If the exponent is omitted, the exponent of that term is equal to 1 
$4 - \sqrt{ 10 } + 2 \sqrt{ 10 } \color{#FF6800}{ - } \left ( \sqrt{ \color{#FF6800}{ 5 } } \right ) ^ { \color{#FF6800}{ 1 } } \sqrt{ 5 }$
$4 - \sqrt{ 10 } + 2 \sqrt{ 10 } - \left ( \sqrt{ 5 } \right ) ^ { 1 } \sqrt{ \color{#FF6800}{ 5 } }$
 If the exponent is omitted, the exponent of that term is equal to 1 
$4 - \sqrt{ 10 } + 2 \sqrt{ 10 } - \left ( \sqrt{ 5 } \right ) ^ { 1 } \left ( \sqrt{ \color{#FF6800}{ 5 } } \right ) ^ { \color{#FF6800}{ 1 } }$
$4 - \sqrt{ 10 } + 2 \sqrt{ 10 } \color{#FF6800}{ - } \left ( \sqrt{ \color{#FF6800}{ 5 } } \right ) ^ { \color{#FF6800}{ 1 } } \left ( \sqrt{ \color{#FF6800}{ 5 } } \right ) ^ { \color{#FF6800}{ 1 } }$
 Add the exponent as the base is the same 
$4 - \sqrt{ 10 } + 2 \sqrt{ 10 } \color{#FF6800}{ - } \left ( \sqrt{ \color{#FF6800}{ 5 } } \right ) ^ { \color{#FF6800}{ 1 } \color{#FF6800}{ + } \color{#FF6800}{ 1 } }$
$4 - \sqrt{ 10 } + 2 \sqrt{ 10 } - \left ( \sqrt{ 5 } \right ) ^ { \color{#FF6800}{ 1 } \color{#FF6800}{ + } \color{#FF6800}{ 1 } }$
 Add $1$ and $1$
$4 - \sqrt{ 10 } + 2 \sqrt{ 10 } - \left ( \sqrt{ 5 } \right ) ^ { \color{#FF6800}{ 2 } }$
$4 - \sqrt{ 10 } + 2 \sqrt{ 10 } - \left ( \sqrt{ \color{#FF6800}{ 5 } } \right ) ^ { \color{#FF6800}{ 2 } }$
 If you square the radical sign, it will disappear 
$4 - \sqrt{ 10 } + 2 \sqrt{ 10 } - \color{#FF6800}{ 5 }$
$\color{#FF6800}{ 4 } - \sqrt{ 10 } + 2 \sqrt{ 10 } \color{#FF6800}{ - } \color{#FF6800}{ 5 }$
 Subtract $5$ from $4$
$\color{#FF6800}{ - } \color{#FF6800}{ 1 } - \sqrt{ 10 } + 2 \sqrt{ 10 }$
$- 1 \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 10 } } \color{#FF6800}{ + } \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 10 } }$
 Calculate between similar terms 
$- 1 + \color{#FF6800}{ 1 } \sqrt{ \color{#FF6800}{ 10 } }$
$- 1 + \color{#FF6800}{ 1 } \sqrt{ 10 }$
 Multiplying any number by 1 does not change the value 
$- 1 + \sqrt{ 10 }$
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