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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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$\left( x+y \right) ^{ 2 } +2 \left( x+y \right) +1$
$\left ( x + y + 1 \right ) ^ { 2 }$
Substitute and transform it into the quadratic expression to arrange an equation
$\left ( \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ y } \right ) ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ 2 } \left ( \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ y } \right ) \color{#FF6800}{ + } \color{#FF6800}{ 1 }$
$ $ Substitute $ x + y $ with $ t$
$\color{#FF6800}{ t } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ 2 } \color{#FF6800}{ t } \color{#FF6800}{ + } \color{#FF6800}{ 1 }$
$\color{#FF6800}{ t } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ 2 } \color{#FF6800}{ t } \color{#FF6800}{ + } \color{#FF6800}{ 1 }$
$ $ Do factorization $ $
$\left ( \color{#FF6800}{ t } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \right ) ^ { \color{#FF6800}{ 2 } }$
$\left ( \color{#FF6800}{ t } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \right ) ^ { \color{#FF6800}{ 2 } }$
$ $ Substitute $ t $ with $ x + y$
$\left ( \left ( \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ y } \right ) \color{#FF6800}{ + } \color{#FF6800}{ 1 } \right ) ^ { \color{#FF6800}{ 2 } }$
$\left ( \left ( \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ y } \right ) \color{#FF6800}{ + } \color{#FF6800}{ 1 } \right ) ^ { 2 }$
$ $ Get rid of unnecessary parentheses $ $
$\left ( \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \right ) ^ { 2 }$
$x ^ { 2 } + 2 x y + 2 x + y ^ { 2 } + 2 y + 1$
Organize polynomials
$\left ( \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ y } \right ) ^ { \color{#FF6800}{ 2 } } + 2 \left ( x + y \right ) + 1$
$ $ Expand the binomial expression $ $
$\color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } + \color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ y } + \color{#FF6800}{ y } ^ { \color{#FF6800}{ 2 } } + 2 \left ( x + y \right ) + 1$
$x ^ { 2 } + 2 x y + y ^ { 2 } + \color{#FF6800}{ 2 } \left ( \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ y } \right ) + 1$
$ $ Use the law of distribution $ $
$x ^ { 2 } + 2 x y + y ^ { 2 } + \color{#FF6800}{ 2 } \color{#FF6800}{ x } + \color{#FF6800}{ 2 } \color{#FF6800}{ y } + 1$
$\color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ y } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 2 } \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ 1 }$
$ $ Sort the polynomial expressions in descending order $ $
$\color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ y } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ 2 } \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ 1 }$
$\left ( x + y + 1 \right ) ^ { 2 }$
Arrange the expression in the form of factorization..
$\left ( \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ y } \right ) ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ 2 } \left ( \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ y } \right ) \color{#FF6800}{ + } \color{#FF6800}{ 1 }$
$ $ Expand the expression $ $
$\color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ y } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ 2 } \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ 1 }$
$\color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ y } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ 2 } \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ 1 }$
$ $ Organize equations using specific formulas $ $
$\left ( \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \right ) ^ { \color{#FF6800}{ 2 } }$
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