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Organize by substituting the expression
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Expand the expression
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Factorize the expression
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$\left( 2x+1 \right) ^{ 2 } -2 \left( 2x+1 \right) -8$
$\left ( 2 x - 3 \right ) \left ( 2 x + 3 \right )$
Substitute and transform it into the quadratic expression to arrange an equation
$\left ( \color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \right ) ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \left ( \color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \right ) \color{#FF6800}{ - } \color{#FF6800}{ 8 }$
$ $ Substitute $ 2 x + 1 $ with $ t$
$\color{#FF6800}{ t } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ t } \color{#FF6800}{ - } \color{#FF6800}{ 8 }$
$\color{#FF6800}{ t } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ t } \color{#FF6800}{ - } \color{#FF6800}{ 8 }$
$ $ Do factorization $ $
$\left ( \color{#FF6800}{ t } \color{#FF6800}{ - } \color{#FF6800}{ 4 } \right ) \left ( \color{#FF6800}{ t } \color{#FF6800}{ + } \color{#FF6800}{ 2 } \right )$
$\left ( \color{#FF6800}{ t } \color{#FF6800}{ - } \color{#FF6800}{ 4 } \right ) \left ( \color{#FF6800}{ t } \color{#FF6800}{ + } \color{#FF6800}{ 2 } \right )$
$ $ Substitute $ t $ with $ 2 x + 1$
$\left ( \left ( \color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \right ) \color{#FF6800}{ - } \color{#FF6800}{ 4 } \right ) \left ( \left ( \color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \right ) \color{#FF6800}{ + } \color{#FF6800}{ 2 } \right )$
$\left ( \left ( \color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \right ) \color{#FF6800}{ - } \color{#FF6800}{ 4 } \right ) \left ( \left ( 2 x + 1 \right ) + 2 \right )$
$ $ Get rid of unnecessary parentheses $ $
$\left ( \color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \color{#FF6800}{ - } \color{#FF6800}{ 4 } \right ) \left ( \left ( 2 x + 1 \right ) + 2 \right )$
$\left ( 2 x + 1 - 4 \right ) \left ( \left ( \color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \right ) \color{#FF6800}{ + } \color{#FF6800}{ 2 } \right )$
$ $ Get rid of unnecessary parentheses $ $
$\left ( 2 x + 1 - 4 \right ) \left ( \color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \color{#FF6800}{ + } \color{#FF6800}{ 2 } \right )$
$\left ( 2 x + \color{#FF6800}{ 1 } \color{#FF6800}{ - } \color{#FF6800}{ 4 } \right ) \left ( 2 x + 1 + 2 \right )$
$ $ Subtract $ 4 $ from $ 1$
$\left ( 2 x \color{#FF6800}{ - } \color{#FF6800}{ 3 } \right ) \left ( 2 x + 1 + 2 \right )$
$\left ( 2 x - 3 \right ) \left ( 2 x + \color{#FF6800}{ 1 } \color{#FF6800}{ + } \color{#FF6800}{ 2 } \right )$
$ $ Add $ 1 $ and $ 2$
$\left ( 2 x - 3 \right ) \left ( 2 x + \color{#FF6800}{ 3 } \right )$
$4 x ^ { 2 } - 9$
Organize polynomials
$\left ( \color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \right ) ^ { \color{#FF6800}{ 2 } } - 2 \left ( 2 x + 1 \right ) - 8$
$ $ Expand the binomial expression $ $
$\color{#FF6800}{ 4 } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } + \color{#FF6800}{ 4 } \color{#FF6800}{ x } + \color{#FF6800}{ 1 } - 2 \left ( 2 x + 1 \right ) - 8$
$4 x ^ { 2 } + 4 x + 1 \color{#FF6800}{ - } \color{#FF6800}{ 2 } \left ( \color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \right ) - 8$
$ $ Organize the expression with the distributive law $ $
$4 x ^ { 2 } + 4 x + 1 \color{#FF6800}{ - } \color{#FF6800}{ 4 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 2 } - 8$
$\color{#FF6800}{ 4 } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ 4 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \color{#FF6800}{ - } \color{#FF6800}{ 4 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ - } \color{#FF6800}{ 8 }$
$ $ Organize the similar terms $ $
$\color{#FF6800}{ 4 } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \left ( \color{#FF6800}{ 4 } \color{#FF6800}{ - } \color{#FF6800}{ 4 } \right ) \color{#FF6800}{ x } \color{#FF6800}{ + } \left ( \color{#FF6800}{ 1 } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ - } \color{#FF6800}{ 8 } \right )$
$4 x ^ { 2 } + \left ( \color{#FF6800}{ 4 } \color{#FF6800}{ - } \color{#FF6800}{ 4 } \right ) \color{#FF6800}{ x } + \left ( 1 - 2 - 8 \right )$
$ $ Organize the mononomial expression $ $
$4 x ^ { 2 } + \color{#FF6800}{ 0 } + \left ( 1 - 2 - 8 \right )$
$4 x ^ { 2 } + 0 + \left ( \color{#FF6800}{ 1 } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ - } \color{#FF6800}{ 8 } \right )$
$ $ Arrange the constant term $ $
$4 x ^ { 2 } + 0 \color{#FF6800}{ - } \color{#FF6800}{ 9 }$
$4 x ^ { 2 } \color{#FF6800}{ + } \color{#FF6800}{ 0 } - 9$
$ $ 0 does not change when you add or subtract $ $
$4 x ^ { 2 } - 9$
$\left ( 2 x - 3 \right ) \left ( 2 x + 3 \right )$
Arrange the expression in the form of factorization..
$\left ( \color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \right ) ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \left ( \color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \right ) \color{#FF6800}{ - } \color{#FF6800}{ 8 }$
$ $ Expand the expression $ $
$\color{#FF6800}{ 4 } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ 9 }$
$\color{#FF6800}{ 4 } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ 9 }$
$ $ Factorize to use the polynomial formula of sum and difference $ $
$\left ( \color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 3 } \right ) \left ( \color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 3 } \right )$
$\left ( \color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 3 } \right ) \left ( \color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 3 } \right )$
$ $ Sort the factors $ $
$\left ( \color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 3 } \right ) \left ( \color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 3 } \right )$
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