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Formula
Calculate the value
Answer
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$\left( 1+ \sqrt{ 3 } \right) ^{ 2 } -2 \left( 1+ \sqrt{ 3 } \right) +1- \left( 1- \sqrt{ 3 } \right) ^{ 2 }$
$- 1 + 2 \sqrt{ 3 }$
Calculate the value
$\left ( \color{#FF6800}{ 1 } \color{#FF6800}{ + } \sqrt{ \color{#FF6800}{ 3 } } \right ) ^ { \color{#FF6800}{ 2 } } - 2 \left ( 1 + \sqrt{ 3 } \right ) + 1 - \left ( 1 - \sqrt{ 3 } \right ) ^ { 2 }$
$ $ Calculate power $ $
$\color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 3 } } + \color{#FF6800}{ 4 } - 2 \left ( 1 + \sqrt{ 3 } \right ) + 1 - \left ( 1 - \sqrt{ 3 } \right ) ^ { 2 }$
$2 \sqrt{ 3 } + 4 \color{#FF6800}{ - } \color{#FF6800}{ 2 } \left ( \color{#FF6800}{ 1 } \color{#FF6800}{ + } \sqrt{ \color{#FF6800}{ 3 } } \right ) + 1 - \left ( 1 - \sqrt{ 3 } \right ) ^ { 2 }$
$ $ Multiply each term in parentheses by $ - 2$
$2 \sqrt{ 3 } + 4 \color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 3 } } + 1 - \left ( 1 - \sqrt{ 3 } \right ) ^ { 2 }$
$2 \sqrt{ 3 } + 4 - 2 - 2 \sqrt{ 3 } + 1 - \left ( \color{#FF6800}{ 1 } \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 3 } } \right ) ^ { \color{#FF6800}{ 2 } }$
$ $ Calculate power $ $
$2 \sqrt{ 3 } + 4 - 2 - 2 \sqrt{ 3 } + 1 - \left ( \color{#FF6800}{ 4 } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 3 } } \right )$
$2 \sqrt{ 3 } + 4 - 2 - 2 \sqrt{ 3 } + 1 \color{#FF6800}{ - } \left ( \color{#FF6800}{ 4 } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 3 } } \right )$
$ $ Change the symbol of each term in parentheses when there is a (-) symbol in front of parentheses $ $
$2 \sqrt{ 3 } + 4 - 2 - 2 \sqrt{ 3 } + 1 \color{#FF6800}{ - } \color{#FF6800}{ 4 } + \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 3 } }$
$2 \sqrt{ 3 } \color{#FF6800}{ + } \color{#FF6800}{ 4 } - 2 - 2 \sqrt{ 3 } + 1 \color{#FF6800}{ - } \color{#FF6800}{ 4 } + 2 \sqrt{ 3 }$
$ $ Remove the two numbers if the values are the same and the signs are different $ $
$2 \sqrt{ 3 } - 2 - 2 \sqrt{ 3 } + 1 + 2 \sqrt{ 3 }$
$\color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 3 } } - \color{#FF6800}{ 2 } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 3 } } + 1 + 2 \sqrt{ 3 }$
$ $ Eliminate opponent number $ $
$- 2 + 1 + 2 \sqrt{ 3 }$
$\color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ + } \color{#FF6800}{ 1 } + 2 \sqrt{ 3 }$
$ $ Add $ - 2 $ and $ 1$
$\color{#FF6800}{ - } \color{#FF6800}{ 1 } + 2 \sqrt{ 3 }$
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