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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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$\left( 2x+y \right) ^{ 2 } - \left( 2x+y \right) -6$
$\left ( 2 x + y - 3 \right ) \left ( 2 x + y + 2 \right )$
Substitute and transform it into the quadratic expression to arrange an equation
$\left ( \color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ y } \right ) ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \left ( \color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ y } \right ) \color{#FF6800}{ - } \color{#FF6800}{ 6 }$
$ $ Substitute $ 2 x + y $ with $ t$
$\color{#FF6800}{ t } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ t } \color{#FF6800}{ - } \color{#FF6800}{ 6 }$
$\color{#FF6800}{ t } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ t } \color{#FF6800}{ - } \color{#FF6800}{ 6 }$
$ $ 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 $ 2 x + y$
$\left ( \left ( \color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ y } \right ) \color{#FF6800}{ - } \color{#FF6800}{ 3 } \right ) \left ( \left ( \color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ y } \right ) \color{#FF6800}{ + } \color{#FF6800}{ 2 } \right )$
$\left ( \left ( \color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ y } \right ) \color{#FF6800}{ - } \color{#FF6800}{ 3 } \right ) \left ( \left ( 2 x + y \right ) + 2 \right )$
$ $ Get rid of unnecessary parentheses $ $
$\left ( \color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ y } \color{#FF6800}{ - } \color{#FF6800}{ 3 } \right ) \left ( \left ( 2 x + y \right ) + 2 \right )$
$\left ( 2 x + y - 3 \right ) \left ( \left ( \color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ y } \right ) \color{#FF6800}{ + } \color{#FF6800}{ 2 } \right )$
$ $ Get rid of unnecessary parentheses $ $
$\left ( 2 x + y - 3 \right ) \left ( \color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ 2 } \right )$
$4 x ^ { 2 } + 4 x y - 2 x + y ^ { 2 } - y - 6$
Organize polynomials
$\left ( \color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ y } \right ) ^ { \color{#FF6800}{ 2 } } - \left ( 2 x + y \right ) - 6$
$ $ Expand the binomial expression $ $
$\color{#FF6800}{ 4 } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } + \color{#FF6800}{ 4 } \color{#FF6800}{ x } \color{#FF6800}{ y } + \color{#FF6800}{ y } ^ { \color{#FF6800}{ 2 } } - \left ( 2 x + y \right ) - 6$
$4 x ^ { 2 } + 4 x y + y ^ { 2 } \color{#FF6800}{ - } \left ( \color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ y } \right ) - 6$
$ $ Change the symbol of each term in parentheses when there is a (-) symbol in front of parentheses $ $
$4 x ^ { 2 } + 4 x y + y ^ { 2 } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ y } - 6$
$\color{#FF6800}{ 4 } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ 4 } \color{#FF6800}{ x } \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ y } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ y } \color{#FF6800}{ - } \color{#FF6800}{ 6 }$
$ $ Sort the polynomial expressions in descending order $ $
$\color{#FF6800}{ 4 } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ 4 } \color{#FF6800}{ x } \color{#FF6800}{ y } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ y } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ y } \color{#FF6800}{ - } \color{#FF6800}{ 6 }$
$\left ( 2 x + y - 3 \right ) \left ( 2 x + y + 2 \right )$
Arrange the expression in the form of factorization..
$\left ( \color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ y } \right ) ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \left ( \color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ y } \right ) \color{#FF6800}{ - } \color{#FF6800}{ 6 }$
$ $ Expand the expression $ $
$\color{#FF6800}{ 4 } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ 4 } \color{#FF6800}{ x } \color{#FF6800}{ y } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ y } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ y } \color{#FF6800}{ - } \color{#FF6800}{ 6 }$
$\color{#FF6800}{ 4 } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ 4 } \color{#FF6800}{ x } \color{#FF6800}{ y } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ y } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ y } \color{#FF6800}{ - } \color{#FF6800}{ 6 }$
$ $ Do factorization $ $
$\left ( \color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ y } \color{#FF6800}{ - } \color{#FF6800}{ 3 } \right ) \left ( \color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ 2 } \right )$
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