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Organize by substituting the expression
Answer
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Expand the expression
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Factorize the expression
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$\left( x+y \right) ^{ 2 } -5 \left( x+y \right) +6$
$\left ( x + y - 3 \right ) \left ( x + y - 2 \right )$
Substitute and transform it into the quadratic expression to arrange an equation
$\left ( \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ y } \right ) ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ 5 } \left ( \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ y } \right ) \color{#FF6800}{ + } \color{#FF6800}{ 6 }$
$ $ Substitute $ x + y $ with $ t$
$\color{#FF6800}{ t } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ 5 } \color{#FF6800}{ t } \color{#FF6800}{ + } \color{#FF6800}{ 6 }$
$\color{#FF6800}{ t } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ 5 } \color{#FF6800}{ t } \color{#FF6800}{ + } \color{#FF6800}{ 6 }$
$ $ Do factorization $ $
$\left ( \color{#FF6800}{ t } \color{#FF6800}{ - } \color{#FF6800}{ 3 } \right ) \left ( \color{#FF6800}{ t } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \right )$
$\left ( \color{#FF6800}{ t } \color{#FF6800}{ - } \color{#FF6800}{ 3 } \right ) \left ( \color{#FF6800}{ t } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \right )$
$ $ Substitute $ t $ with $ x + y$
$\left ( \left ( \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ y } \right ) \color{#FF6800}{ - } \color{#FF6800}{ 3 } \right ) \left ( \left ( \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ y } \right ) \color{#FF6800}{ - } \color{#FF6800}{ 2 } \right )$
$\left ( \left ( \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ y } \right ) \color{#FF6800}{ - } \color{#FF6800}{ 3 } \right ) \left ( \left ( x + y \right ) - 2 \right )$
$ $ Get rid of unnecessary parentheses $ $
$\left ( \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ y } \color{#FF6800}{ - } \color{#FF6800}{ 3 } \right ) \left ( \left ( x + y \right ) - 2 \right )$
$\left ( x + y - 3 \right ) \left ( \left ( \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ y } \right ) \color{#FF6800}{ - } \color{#FF6800}{ 2 } \right )$
$ $ Get rid of unnecessary parentheses $ $
$\left ( x + y - 3 \right ) \left ( \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ y } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \right )$
$x ^ { 2 } + 2 x y - 5 x + y ^ { 2 } - 5 y + 6$
Organize polynomials
$\left ( \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ y } \right ) ^ { \color{#FF6800}{ 2 } } - 5 \left ( x + y \right ) + 6$
$ $ Expand the binomial expression $ $
$\color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } + \color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ y } + \color{#FF6800}{ y } ^ { \color{#FF6800}{ 2 } } - 5 \left ( x + y \right ) + 6$
$x ^ { 2 } + 2 x y + y ^ { 2 } \color{#FF6800}{ - } \color{#FF6800}{ 5 } \left ( \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ y } \right ) + 6$
$ $ Use the law of distribution $ $
$x ^ { 2 } + 2 x y + y ^ { 2 } \color{#FF6800}{ - } \color{#FF6800}{ 5 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 5 } \color{#FF6800}{ y } + 6$
$\color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ y } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ 5 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 5 } \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ 6 }$
$ $ Sort the polynomial expressions in descending order $ $
$\color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ y } \color{#FF6800}{ - } \color{#FF6800}{ 5 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ y } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ 5 } \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ 6 }$
$\left ( x + y - 3 \right ) \left ( x + y - 2 \right )$
Arrange the expression in the form of factorization..
$\left ( \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ y } \right ) ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ 5 } \left ( \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ y } \right ) \color{#FF6800}{ + } \color{#FF6800}{ 6 }$
$ $ Expand the expression $ $
$\color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ y } \color{#FF6800}{ - } \color{#FF6800}{ 5 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ y } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ 5 } \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ 6 }$
$\color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ y } \color{#FF6800}{ - } \color{#FF6800}{ 5 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ y } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ 5 } \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ 6 }$
$ $ Do factorization $ $
$\left ( \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ y } \color{#FF6800}{ - } \color{#FF6800}{ 3 } \right ) \left ( \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ y } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \right )$
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