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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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$\left( x+3 \right) ^{ 2 } -2 \left( x+3 \right) -24$
$\left ( x - 3 \right ) \left ( x + 7 \right )$
Substitute and transform it into the quadratic expression to arrange an equation
$\left ( \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 3 } \right ) ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \left ( \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 3 } \right ) \color{#FF6800}{ - } \color{#FF6800}{ 24 }$
$ $ Substitute $ x + 3 $ with $ t$
$\color{#FF6800}{ t } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ t } \color{#FF6800}{ - } \color{#FF6800}{ 24 }$
$\color{#FF6800}{ t } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ t } \color{#FF6800}{ - } \color{#FF6800}{ 24 }$
$ $ Do factorization $ $
$\left ( \color{#FF6800}{ t } \color{#FF6800}{ - } \color{#FF6800}{ 6 } \right ) \left ( \color{#FF6800}{ t } \color{#FF6800}{ + } \color{#FF6800}{ 4 } \right )$
$\left ( \color{#FF6800}{ t } \color{#FF6800}{ - } \color{#FF6800}{ 6 } \right ) \left ( \color{#FF6800}{ t } \color{#FF6800}{ + } \color{#FF6800}{ 4 } \right )$
$ $ Substitute $ t $ with $ x + 3$
$\left ( \left ( \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 3 } \right ) \color{#FF6800}{ - } \color{#FF6800}{ 6 } \right ) \left ( \left ( \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 3 } \right ) \color{#FF6800}{ + } \color{#FF6800}{ 4 } \right )$
$\left ( \left ( \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 3 } \right ) \color{#FF6800}{ - } \color{#FF6800}{ 6 } \right ) \left ( \left ( x + 3 \right ) + 4 \right )$
$ $ Get rid of unnecessary parentheses $ $
$\left ( \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 3 } \color{#FF6800}{ - } \color{#FF6800}{ 6 } \right ) \left ( \left ( x + 3 \right ) + 4 \right )$
$\left ( x + 3 - 6 \right ) \left ( \left ( \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 3 } \right ) \color{#FF6800}{ + } \color{#FF6800}{ 4 } \right )$
$ $ Get rid of unnecessary parentheses $ $
$\left ( x + 3 - 6 \right ) \left ( \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 3 } \color{#FF6800}{ + } \color{#FF6800}{ 4 } \right )$
$\left ( x + \color{#FF6800}{ 3 } \color{#FF6800}{ - } \color{#FF6800}{ 6 } \right ) \left ( x + 3 + 4 \right )$
$ $ Subtract $ 6 $ from $ 3$
$\left ( x \color{#FF6800}{ - } \color{#FF6800}{ 3 } \right ) \left ( x + 3 + 4 \right )$
$\left ( x - 3 \right ) \left ( x + \color{#FF6800}{ 3 } \color{#FF6800}{ + } \color{#FF6800}{ 4 } \right )$
$ $ Add $ 3 $ and $ 4$
$\left ( x - 3 \right ) \left ( x + \color{#FF6800}{ 7 } \right )$
$x ^ { 2 } + 4 x - 21$
Organize polynomials
$\left ( \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 3 } \right ) ^ { \color{#FF6800}{ 2 } } - 2 \left ( x + 3 \right ) - 24$
$ $ Expand the binomial expression $ $
$\color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } + \color{#FF6800}{ 6 } \color{#FF6800}{ x } + \color{#FF6800}{ 9 } - 2 \left ( x + 3 \right ) - 24$
$x ^ { 2 } + 6 x + 9 \color{#FF6800}{ - } \color{#FF6800}{ 2 } \left ( \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 3 } \right ) - 24$
$ $ Organize the expression with the distributive law $ $
$x ^ { 2 } + 6 x + 9 \color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 6 } - 24$
$\color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ 6 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 9 } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 6 } \color{#FF6800}{ - } \color{#FF6800}{ 24 }$
$ $ Organize the similar terms $ $
$\color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \left ( \color{#FF6800}{ 6 } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \right ) \color{#FF6800}{ x } \color{#FF6800}{ + } \left ( \color{#FF6800}{ 9 } \color{#FF6800}{ - } \color{#FF6800}{ 6 } \color{#FF6800}{ - } \color{#FF6800}{ 24 } \right )$
$x ^ { 2 } + \left ( \color{#FF6800}{ 6 } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \right ) \color{#FF6800}{ x } + \left ( 9 - 6 - 24 \right )$
$ $ Arrange the constant term $ $
$x ^ { 2 } + \color{#FF6800}{ 4 } \color{#FF6800}{ x } + \left ( 9 - 6 - 24 \right )$
$x ^ { 2 } + 4 x + \left ( \color{#FF6800}{ 9 } \color{#FF6800}{ - } \color{#FF6800}{ 6 } \color{#FF6800}{ - } \color{#FF6800}{ 24 } \right )$
$ $ Arrange the constant term $ $
$x ^ { 2 } + 4 x \color{#FF6800}{ - } \color{#FF6800}{ 21 }$
$\left ( x - 3 \right ) \left ( x + 7 \right )$
Arrange the expression in the form of factorization..
$\left ( \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 3 } \right ) ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \left ( \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 3 } \right ) \color{#FF6800}{ - } \color{#FF6800}{ 24 }$
$ $ Expand the expression $ $
$\color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ 4 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 21 }$
$\color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ 4 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 21 }$
$ $ Use the factoring formula, $ x^{2} + \left(a+b\right)x + ab = \left(x+a\right)\left(x+b\right)$
$\left ( \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 7 } \right ) \left ( \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 3 } \right )$
$\left ( \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 7 } \right ) \left ( \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 3 } \right )$
$ $ Sort the factors $ $
$\left ( \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 3 } \right ) \left ( \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 7 } \right )$
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