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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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$\left( x+1 \right) ^{ 2 } -4 \left( x+1 \right) +4$
$\left ( x - 1 \right ) ^ { 2 }$
Substitute and transform it into the quadratic expression to arrange an equation
$\left ( \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \right ) ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ 4 } \left ( \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \right ) \color{#FF6800}{ + } \color{#FF6800}{ 4 }$
$ $ Substitute $ x + 1 $ with $ t$
$\color{#FF6800}{ t } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ 4 } \color{#FF6800}{ t } \color{#FF6800}{ + } \color{#FF6800}{ 4 }$
$\color{#FF6800}{ t } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ 4 } \color{#FF6800}{ t } \color{#FF6800}{ + } \color{#FF6800}{ 4 }$
$ $ Do factorization $ $
$\left ( \color{#FF6800}{ t } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \right ) ^ { \color{#FF6800}{ 2 } }$
$\left ( \color{#FF6800}{ t } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \right ) ^ { \color{#FF6800}{ 2 } }$
$ $ Substitute $ t $ with $ x + 1$
$\left ( \left ( \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \right ) \color{#FF6800}{ - } \color{#FF6800}{ 2 } \right ) ^ { \color{#FF6800}{ 2 } }$
$\left ( \left ( \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \right ) \color{#FF6800}{ - } \color{#FF6800}{ 2 } \right ) ^ { 2 }$
$ $ Get rid of unnecessary parentheses $ $
$\left ( \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \right ) ^ { 2 }$
$\left ( x + \color{#FF6800}{ 1 } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \right ) ^ { 2 }$
$ $ Subtract $ 2 $ from $ 1$
$\left ( x \color{#FF6800}{ - } \color{#FF6800}{ 1 } \right ) ^ { 2 }$
$x ^ { 2 } - 2 x + 1$
Organize polynomials
$\left ( \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \right ) ^ { \color{#FF6800}{ 2 } } - 4 \left ( x + 1 \right ) + 4$
$ $ Expand the binomial expression $ $
$\color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } + \color{#FF6800}{ 2 } \color{#FF6800}{ x } + \color{#FF6800}{ 1 } - 4 \left ( x + 1 \right ) + 4$
$x ^ { 2 } + 2 x + 1 \color{#FF6800}{ - } \color{#FF6800}{ 4 } \left ( \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \right ) + 4$
$ $ Organize the expression with the distributive law $ $
$x ^ { 2 } + 2 x + 1 \color{#FF6800}{ - } \color{#FF6800}{ 4 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 4 } + 4$
$\color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \color{#FF6800}{ - } \color{#FF6800}{ 4 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 4 } \color{#FF6800}{ + } \color{#FF6800}{ 4 }$
$ $ Organize the similar terms $ $
$\color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \left ( \color{#FF6800}{ 2 } \color{#FF6800}{ - } \color{#FF6800}{ 4 } \right ) \color{#FF6800}{ x } \color{#FF6800}{ + } \left ( \color{#FF6800}{ 1 } \color{#FF6800}{ - } \color{#FF6800}{ 4 } \color{#FF6800}{ + } \color{#FF6800}{ 4 } \right )$
$x ^ { 2 } + \left ( \color{#FF6800}{ 2 } \color{#FF6800}{ - } \color{#FF6800}{ 4 } \right ) \color{#FF6800}{ x } + \left ( 1 - 4 + 4 \right )$
$ $ Arrange the constant term $ $
$x ^ { 2 } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ x } + \left ( 1 - 4 + 4 \right )$
$x ^ { 2 } - 2 x + \left ( \color{#FF6800}{ 1 } \color{#FF6800}{ - } \color{#FF6800}{ 4 } \color{#FF6800}{ + } \color{#FF6800}{ 4 } \right )$
$ $ Arrange the constant term $ $
$x ^ { 2 } - 2 x + \color{#FF6800}{ 1 }$
$\left ( x - 1 \right ) ^ { 2 }$
Arrange the expression in the form of factorization..
$\left ( \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \right ) ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ 4 } \left ( \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \right ) \color{#FF6800}{ + } \color{#FF6800}{ 4 }$
$ $ Expand the expression $ $
$\color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 1 }$
$\color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 1 }$
$ $ Use the factoring formula, $ a^{2}-2ab + b^{2} = \left(a-b\right)^{2}$
$\left ( \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 1 } \right ) ^ { \color{#FF6800}{ 2 } }$
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