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Expand the expression
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Factorize the expression
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$3 x ^ { 2 } - 8 x y - 3 y ^ { 2 }$
Organize polynomials
$\left ( \color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ y } \right ) ^ { \color{#FF6800}{ 2 } } - \left ( x + 2 y \right ) ^ { 2 }$
$ $ Expand the binomial expression $ $
$\color{#FF6800}{ 4 } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ 4 } \color{#FF6800}{ x } \color{#FF6800}{ y } + \color{#FF6800}{ y } ^ { \color{#FF6800}{ 2 } } - \left ( x + 2 y \right ) ^ { 2 }$
$4 x ^ { 2 } - 4 x y + y ^ { 2 } - \left ( \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 2 } \color{#FF6800}{ y } \right ) ^ { \color{#FF6800}{ 2 } }$
$ $ Expand the binomial expression $ $
$4 x ^ { 2 } - 4 x y + y ^ { 2 } - \left ( \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ 4 } \color{#FF6800}{ x } \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ 4 } \color{#FF6800}{ y } ^ { \color{#FF6800}{ 2 } } \right )$
$4 x ^ { 2 } - 4 x y + y ^ { 2 } \color{#FF6800}{ - } \left ( \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ 4 } \color{#FF6800}{ x } \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ 4 } \color{#FF6800}{ y } ^ { \color{#FF6800}{ 2 } } \right )$
$ $ Change the symbol of each term in parentheses when there is a (-) symbol in front of parentheses $ $
$4 x ^ { 2 } - 4 x y + y ^ { 2 } \color{#FF6800}{ - } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ 4 } \color{#FF6800}{ x } \color{#FF6800}{ y } \color{#FF6800}{ - } \color{#FF6800}{ 4 } \color{#FF6800}{ y } ^ { \color{#FF6800}{ 2 } }$
$\color{#FF6800}{ 4 } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ 4 } \color{#FF6800}{ x } \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ y } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ 4 } \color{#FF6800}{ x } \color{#FF6800}{ y } \color{#FF6800}{ - } \color{#FF6800}{ 4 } \color{#FF6800}{ y } ^ { \color{#FF6800}{ 2 } }$
$ $ Organize the similar terms $ $
$\left ( \color{#FF6800}{ 4 } \color{#FF6800}{ - } \color{#FF6800}{ 1 } \right ) \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 4 } \color{#FF6800}{ - } \color{#FF6800}{ 4 } \right ) \color{#FF6800}{ x } \color{#FF6800}{ y } \color{#FF6800}{ + } \left ( \color{#FF6800}{ 1 } \color{#FF6800}{ - } \color{#FF6800}{ 4 } \right ) \color{#FF6800}{ y } ^ { \color{#FF6800}{ 2 } }$
$\left ( \color{#FF6800}{ 4 } \color{#FF6800}{ - } \color{#FF6800}{ 1 } \right ) \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } + \left ( - 4 - 4 \right ) x y + \left ( 1 - 4 \right ) y ^ { 2 }$
$ $ Arrange the constant term $ $
$\color{#FF6800}{ 3 } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } + \left ( - 4 - 4 \right ) x y + \left ( 1 - 4 \right ) y ^ { 2 }$
$3 x ^ { 2 } + \left ( \color{#FF6800}{ - } \color{#FF6800}{ 4 } \color{#FF6800}{ - } \color{#FF6800}{ 4 } \right ) \color{#FF6800}{ x } \color{#FF6800}{ y } + \left ( 1 - 4 \right ) y ^ { 2 }$
$ $ Arrange the constant term $ $
$3 x ^ { 2 } \color{#FF6800}{ - } \color{#FF6800}{ 8 } \color{#FF6800}{ x } \color{#FF6800}{ y } + \left ( 1 - 4 \right ) y ^ { 2 }$
$3 x ^ { 2 } - 8 x y + \left ( \color{#FF6800}{ 1 } \color{#FF6800}{ - } \color{#FF6800}{ 4 } \right ) \color{#FF6800}{ y } ^ { \color{#FF6800}{ 2 } }$
$ $ Arrange the constant term $ $
$3 x ^ { 2 } - 8 x y \color{#FF6800}{ - } \color{#FF6800}{ 3 } \color{#FF6800}{ y } ^ { \color{#FF6800}{ 2 } }$
$\left ( x - 3 y \right ) \left ( 3 x + y \right )$
Arrange the expression in the form of factorization..
$\left ( \color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ y } \right ) ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \left ( \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 2 } \color{#FF6800}{ y } \right ) ^ { \color{#FF6800}{ 2 } }$
$ $ Factorize to use the polynomial formula of sum and difference $ $
$\left ( \color{#FF6800}{ 3 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ y } \right ) \left ( \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 3 } \color{#FF6800}{ y } \right )$
$\left ( \color{#FF6800}{ 3 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ y } \right ) \left ( \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 3 } \color{#FF6800}{ y } \right )$
$ $ Sort the factors $ $
$\left ( \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 3 } \color{#FF6800}{ y } \right ) \left ( \color{#FF6800}{ 3 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ y } \right )$
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