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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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$2 \left( 5x+1 \right) ^{ 2 } -5 \left( 5x+1 \right) -3$
$\left ( 5 x - 2 \right ) \left ( 10 x + 3 \right )$
Substitute and transform it into the quadratic expression to arrange an equation
$\color{#FF6800}{ 2 } \left ( \color{#FF6800}{ 5 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \right ) ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ 5 } \left ( \color{#FF6800}{ 5 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \right ) \color{#FF6800}{ - } \color{#FF6800}{ 3 }$
$ $ Substitute $ 5 x + 1 $ with $ t$
$\color{#FF6800}{ 2 } \color{#FF6800}{ t } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ 5 } \color{#FF6800}{ t } \color{#FF6800}{ - } \color{#FF6800}{ 3 }$
$\color{#FF6800}{ 2 } \color{#FF6800}{ t } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ 5 } \color{#FF6800}{ t } \color{#FF6800}{ - } \color{#FF6800}{ 3 }$
$ $ Do factorization $ $
$\left ( \color{#FF6800}{ t } \color{#FF6800}{ - } \color{#FF6800}{ 3 } \right ) \left ( \color{#FF6800}{ 2 } \color{#FF6800}{ t } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \right )$
$\left ( \color{#FF6800}{ t } \color{#FF6800}{ - } \color{#FF6800}{ 3 } \right ) \left ( \color{#FF6800}{ 2 } \color{#FF6800}{ t } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \right )$
$ $ Substitute $ t $ with $ 5 x + 1$
$\left ( \left ( \color{#FF6800}{ 5 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \right ) \color{#FF6800}{ - } \color{#FF6800}{ 3 } \right ) \left ( \color{#FF6800}{ 2 } \left ( \color{#FF6800}{ 5 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \right ) \color{#FF6800}{ + } \color{#FF6800}{ 1 } \right )$
$\left ( \left ( \color{#FF6800}{ 5 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \right ) \color{#FF6800}{ - } \color{#FF6800}{ 3 } \right ) \left ( 2 \left ( 5 x + 1 \right ) + 1 \right )$
$ $ Get rid of unnecessary parentheses $ $
$\left ( \color{#FF6800}{ 5 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \color{#FF6800}{ - } \color{#FF6800}{ 3 } \right ) \left ( 2 \left ( 5 x + 1 \right ) + 1 \right )$
$\left ( 5 x + \color{#FF6800}{ 1 } \color{#FF6800}{ - } \color{#FF6800}{ 3 } \right ) \left ( 2 \left ( 5 x + 1 \right ) + 1 \right )$
$ $ Subtract $ 3 $ from $ 1$
$\left ( 5 x \color{#FF6800}{ - } \color{#FF6800}{ 2 } \right ) \left ( 2 \left ( 5 x + 1 \right ) + 1 \right )$
$\left ( 5 x - 2 \right ) \left ( \color{#FF6800}{ 2 } \left ( \color{#FF6800}{ 5 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \right ) \color{#FF6800}{ + } \color{#FF6800}{ 1 } \right )$
$ $ Do factorization $ $
$\left ( 5 x - 2 \right ) \left ( \color{#FF6800}{ 10 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 3 } \right )$
$50 x ^ { 2 } - 5 x - 6$
Organize polynomials
$2 \left ( \color{#FF6800}{ 5 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \right ) ^ { \color{#FF6800}{ 2 } } - 5 \left ( 5 x + 1 \right ) - 3$
$ $ Expand the binomial expression $ $
$2 \left ( \color{#FF6800}{ 25 } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ 10 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \right ) - 5 \left ( 5 x + 1 \right ) - 3$
$\color{#FF6800}{ 2 } \left ( \color{#FF6800}{ 25 } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ 10 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \right ) - 5 \left ( 5 x + 1 \right ) - 3$
$ $ Organize the expression with the distributive law $ $
$\color{#FF6800}{ 50 } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } + \color{#FF6800}{ 20 } \color{#FF6800}{ x } + \color{#FF6800}{ 2 } - 5 \left ( 5 x + 1 \right ) - 3$
$50 x ^ { 2 } + 20 x + 2 \color{#FF6800}{ - } \color{#FF6800}{ 5 } \left ( \color{#FF6800}{ 5 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \right ) - 3$
$ $ Organize the expression with the distributive law $ $
$50 x ^ { 2 } + 20 x + 2 \color{#FF6800}{ - } \color{#FF6800}{ 25 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 5 } - 3$
$\color{#FF6800}{ 50 } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ 20 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 2 } \color{#FF6800}{ - } \color{#FF6800}{ 25 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 5 } \color{#FF6800}{ - } \color{#FF6800}{ 3 }$
$ $ Organize the similar terms $ $
$\color{#FF6800}{ 50 } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \left ( \color{#FF6800}{ 20 } \color{#FF6800}{ - } \color{#FF6800}{ 25 } \right ) \color{#FF6800}{ x } \color{#FF6800}{ + } \left ( \color{#FF6800}{ 2 } \color{#FF6800}{ - } \color{#FF6800}{ 5 } \color{#FF6800}{ - } \color{#FF6800}{ 3 } \right )$
$50 x ^ { 2 } + \left ( \color{#FF6800}{ 20 } \color{#FF6800}{ - } \color{#FF6800}{ 25 } \right ) \color{#FF6800}{ x } + \left ( 2 - 5 - 3 \right )$
$ $ Arrange the constant term $ $
$50 x ^ { 2 } \color{#FF6800}{ - } \color{#FF6800}{ 5 } \color{#FF6800}{ x } + \left ( 2 - 5 - 3 \right )$
$50 x ^ { 2 } - 5 x + \left ( \color{#FF6800}{ 2 } \color{#FF6800}{ - } \color{#FF6800}{ 5 } \color{#FF6800}{ - } \color{#FF6800}{ 3 } \right )$
$ $ Arrange the constant term $ $
$50 x ^ { 2 } - 5 x \color{#FF6800}{ - } \color{#FF6800}{ 6 }$
$\left ( 5 x - 2 \right ) \left ( 10 x + 3 \right )$
Arrange the expression in the form of factorization..
$\color{#FF6800}{ 2 } \left ( \color{#FF6800}{ 5 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \right ) ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ 5 } \left ( \color{#FF6800}{ 5 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \right ) \color{#FF6800}{ - } \color{#FF6800}{ 3 }$
$ $ Expand the expression $ $
$\color{#FF6800}{ 50 } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ 5 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 6 }$
$\color{#FF6800}{ 50 } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ 5 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 6 }$
$ $ Use the factoring formula, $ acx^{2} + \left(ad + bc\right)x + bd = \left(ax+b\right)\left(cx+d\right)$
$\left ( \color{#FF6800}{ 10 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 3 } \right ) \left ( \color{#FF6800}{ 5 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \right )$
$\left ( \color{#FF6800}{ 10 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 3 } \right ) \left ( \color{#FF6800}{ 5 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \right )$
$ $ Sort the factors $ $
$\left ( \color{#FF6800}{ 5 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \right ) \left ( \color{#FF6800}{ 10 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 3 } \right )$
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