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Expand the expression
Answer
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Factorize the expression
Answer
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$x ^{ 2 } \left( y-z \right) +y ^{ 2 } \left( z-x \right) +z ^{ 2 } \left( x-y \right)$
$x ^ { 2 } y - x ^ { 2 } z - x y ^ { 2 } + x z ^ { 2 } + y ^ { 2 } z - y z ^ { 2 }$
Organize polynomials
$\color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \left ( \color{#FF6800}{ y } \color{#FF6800}{ - } \color{#FF6800}{ z } \right ) + y ^ { 2 } \left ( z - x \right ) + z ^ { 2 } \left ( x - y \right )$
$ $ Organize the expression with the distributive law $ $
$\color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ y } \color{#FF6800}{ - } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ z } + y ^ { 2 } \left ( z - x \right ) + z ^ { 2 } \left ( x - y \right )$
$x ^ { 2 } y - x ^ { 2 } z + y ^ { 2 } \left ( \color{#FF6800}{ z } \color{#FF6800}{ - } \color{#FF6800}{ x } \right ) + z ^ { 2 } \left ( x - y \right )$
$ $ Sort the polynomial expressions in descending order $ $
$x ^ { 2 } y - x ^ { 2 } z + y ^ { 2 } \left ( \color{#FF6800}{ - } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ z } \right ) + z ^ { 2 } \left ( x - y \right )$
$x ^ { 2 } y - x ^ { 2 } z + \color{#FF6800}{ y } ^ { \color{#FF6800}{ 2 } } \left ( \color{#FF6800}{ - } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ z } \right ) + z ^ { 2 } \left ( x - y \right )$
$ $ Organize the expression with the distributive law $ $
$x ^ { 2 } y - x ^ { 2 } z \color{#FF6800}{ - } \color{#FF6800}{ x } \color{#FF6800}{ y } ^ { \color{#FF6800}{ 2 } } + \color{#FF6800}{ y } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ z } + z ^ { 2 } \left ( x - y \right )$
$x ^ { 2 } y - x ^ { 2 } z - x y ^ { 2 } + y ^ { 2 } z + \color{#FF6800}{ z } ^ { \color{#FF6800}{ 2 } } \left ( \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ y } \right )$
$ $ Organize the expression with the distributive law $ $
$x ^ { 2 } y - x ^ { 2 } z - x y ^ { 2 } + y ^ { 2 } z + \color{#FF6800}{ x } \color{#FF6800}{ z } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ y } \color{#FF6800}{ z } ^ { \color{#FF6800}{ 2 } }$
$\color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ y } \color{#FF6800}{ - } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ z } \color{#FF6800}{ - } \color{#FF6800}{ x } \color{#FF6800}{ y } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ y } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ z } \color{#FF6800}{ + } \color{#FF6800}{ x } \color{#FF6800}{ z } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ y } \color{#FF6800}{ z } ^ { \color{#FF6800}{ 2 } }$
$ $ Sort the polynomial expressions in descending order $ $
$\color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ y } \color{#FF6800}{ - } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ z } \color{#FF6800}{ - } \color{#FF6800}{ x } \color{#FF6800}{ y } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ x } \color{#FF6800}{ z } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ y } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ z } \color{#FF6800}{ - } \color{#FF6800}{ y } \color{#FF6800}{ z } ^ { \color{#FF6800}{ 2 } }$
$\left ( x - y \right ) \left ( x - z \right ) \left ( y - z \right )$
Arrange the expression in the form of factorization..
$\color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \left ( \color{#FF6800}{ y } \color{#FF6800}{ - } \color{#FF6800}{ z } \right ) \color{#FF6800}{ + } \color{#FF6800}{ y } ^ { \color{#FF6800}{ 2 } } \left ( \color{#FF6800}{ z } \color{#FF6800}{ - } \color{#FF6800}{ x } \right ) \color{#FF6800}{ + } \color{#FF6800}{ z } ^ { \color{#FF6800}{ 2 } } \left ( \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ y } \right )$
$ $ Expand the expression $ $
$\color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ y } \color{#FF6800}{ - } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ z } \color{#FF6800}{ - } \color{#FF6800}{ x } \color{#FF6800}{ y } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ x } \color{#FF6800}{ z } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ y } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ z } \color{#FF6800}{ - } \color{#FF6800}{ y } \color{#FF6800}{ z } ^ { \color{#FF6800}{ 2 } }$
$\color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ y } \color{#FF6800}{ - } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ z } \color{#FF6800}{ - } \color{#FF6800}{ x } \color{#FF6800}{ y } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ x } \color{#FF6800}{ z } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ y } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ z } \color{#FF6800}{ - } \color{#FF6800}{ y } \color{#FF6800}{ z } ^ { \color{#FF6800}{ 2 } }$
$ $ Do factorization $ $
$\left ( \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ y } \right ) \left ( \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ z } \right ) \left ( \color{#FF6800}{ y } \color{#FF6800}{ - } \color{#FF6800}{ z } \right )$
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