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Expand the expression

Answer

Factorize the expression

Answer

Organize equations using specific formulas

Answer

$x ^{ 3 } +y ^{ 3 } -z ^{ 3 } +3xyz$

$x ^ { 3 } + 3 x y z + y ^ { 3 } - z ^ { 3 }$

Organize polynomials

$\color{#FF6800}{ x } ^ { \color{#FF6800}{ 3 } } \color{#FF6800}{ + } \color{#FF6800}{ y } ^ { \color{#FF6800}{ 3 } } \color{#FF6800}{ - } \color{#FF6800}{ z } ^ { \color{#FF6800}{ 3 } } \color{#FF6800}{ + } \color{#FF6800}{ 3 } \color{#FF6800}{ x } \color{#FF6800}{ y } \color{#FF6800}{ z }$

$ $ Sort the polynomial expressions in descending order $ $

$\color{#FF6800}{ x } ^ { \color{#FF6800}{ 3 } } \color{#FF6800}{ + } \color{#FF6800}{ 3 } \color{#FF6800}{ x } \color{#FF6800}{ y } \color{#FF6800}{ z } \color{#FF6800}{ + } \color{#FF6800}{ y } ^ { \color{#FF6800}{ 3 } } \color{#FF6800}{ - } \color{#FF6800}{ z } ^ { \color{#FF6800}{ 3 } }$

$\left ( x + y - z \right ) \left ( x ^ { 2 } - x y + x z + y ^ { 2 } + y z + z ^ { 2 } \right )$

Arrange the expression in the form of factorization..

$ $ Arrange an equation using the transformation of the multiplication formula $ $

$\left ( \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ y } \color{#FF6800}{ - } \color{#FF6800}{ z } \right ) \left ( \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ y } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ z } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ x } \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ y } \color{#FF6800}{ z } \color{#FF6800}{ + } \color{#FF6800}{ x } \color{#FF6800}{ z } \right )$

$\left ( x + y - z \right ) \left ( \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ y } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ z } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ x } \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ y } \color{#FF6800}{ z } \color{#FF6800}{ + } \color{#FF6800}{ x } \color{#FF6800}{ z } \right )$

$ $ Organize the expression $ $

$\left ( x + y - z \right ) \left ( \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ x } \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ x } \color{#FF6800}{ z } \color{#FF6800}{ + } \color{#FF6800}{ y } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ y } \color{#FF6800}{ z } \color{#FF6800}{ + } \color{#FF6800}{ z } ^ { \color{#FF6800}{ 2 } } \right )$

$\dfrac { 1 } { 2 } \left ( x + y - z \right ) \left ( \left ( x - y \right ) ^ { 2 } + \left ( y + z \right ) ^ { 2 } + \left ( z + x \right ) ^ { 2 } \right )$

Organize equations using specific formulas

$ $ Transform into the transformation format of the multiplication formula $ $

$\color{#FF6800}{ x } ^ { \color{#FF6800}{ 3 } } \color{#FF6800}{ + } \color{#FF6800}{ y } ^ { \color{#FF6800}{ 3 } } \color{#FF6800}{ - } \color{#FF6800}{ z } ^ { \color{#FF6800}{ 3 } } \color{#FF6800}{ - } \color{#FF6800}{ 3 } \color{#FF6800}{ x } \color{#FF6800}{ y } \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \color{#FF6800}{ z } \right )$

$ $ Factorize to use $ x^{3}+y^{3}+z^{3}-3xyz=(x+y+z)(x^{2}+y^{2}+z^{2}-xy-yx-zx)$

$\left ( \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ y } \color{#FF6800}{ - } \color{#FF6800}{ z } \right ) \left ( \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ y } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \left ( \color{#FF6800}{ - } \color{#FF6800}{ z } \right ) ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ x } \color{#FF6800}{ y } \color{#FF6800}{ - } \color{#FF6800}{ y } \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \color{#FF6800}{ z } \right ) \color{#FF6800}{ - } \color{#FF6800}{ x } \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \color{#FF6800}{ z } \right ) \right )$

$\left ( x + y - z \right ) \left ( \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ y } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \left ( \color{#FF6800}{ - } \color{#FF6800}{ z } \right ) ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ x } \color{#FF6800}{ y } \color{#FF6800}{ - } \color{#FF6800}{ y } \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \color{#FF6800}{ z } \right ) \color{#FF6800}{ - } \color{#FF6800}{ x } \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \color{#FF6800}{ z } \right ) \right )$

$ $ Organize equations using specific formulas $ $

$\left ( x + y - z \right ) \times \color{#FF6800}{ \dfrac { 1 } { 2 } } \left ( \left ( \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ y } \right ) ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \left ( \color{#FF6800}{ y } \color{#FF6800}{ - } \left ( \color{#FF6800}{ - } \color{#FF6800}{ z } \right ) \right ) ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \left ( \color{#FF6800}{ - } \color{#FF6800}{ z } \color{#FF6800}{ - } \color{#FF6800}{ x } \right ) ^ { \color{#FF6800}{ 2 } } \right )$

$\left ( \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ y } \color{#FF6800}{ - } \color{#FF6800}{ z } \right ) \color{#FF6800}{ \times } \color{#FF6800}{ \dfrac { 1 } { 2 } } \left ( \left ( \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ y } \right ) ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \left ( \color{#FF6800}{ y } \color{#FF6800}{ - } \left ( \color{#FF6800}{ - } \color{#FF6800}{ z } \right ) \right ) ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \left ( \color{#FF6800}{ - } \color{#FF6800}{ z } \color{#FF6800}{ - } \color{#FF6800}{ x } \right ) ^ { \color{#FF6800}{ 2 } } \right )$

$ $ Organize the expression $ $

$\color{#FF6800}{ \dfrac { 1 } { 2 } } \left ( \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ y } \color{#FF6800}{ - } \color{#FF6800}{ z } \right ) \left ( \left ( \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ y } \right ) ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \left ( \color{#FF6800}{ y } \color{#FF6800}{ - } \left ( \color{#FF6800}{ - } \color{#FF6800}{ z } \right ) \right ) ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \left ( \color{#FF6800}{ - } \color{#FF6800}{ z } \color{#FF6800}{ - } \color{#FF6800}{ x } \right ) ^ { \color{#FF6800}{ 2 } } \right )$

$\dfrac { 1 } { 2 } \left ( x + y - z \right ) \left ( \left ( x - y \right ) ^ { 2 } + \left ( y \color{#FF6800}{ - } \left ( \color{#FF6800}{ - } z \right ) \right ) ^ { 2 } + \left ( - z - x \right ) ^ { 2 } \right )$

$ $ Simplify Minus $ $

$\dfrac { 1 } { 2 } \left ( x + y - z \right ) \left ( \left ( x - y \right ) ^ { 2 } + \left ( y + z \right ) ^ { 2 } + \left ( - z - x \right ) ^ { 2 } \right )$

$\dfrac { 1 } { 2 } \left ( x + y - z \right ) \left ( \left ( x - y \right ) ^ { 2 } + \left ( y + z \right ) ^ { 2 } + \left ( \color{#FF6800}{ - } \color{#FF6800}{ z } \color{#FF6800}{ - } \color{#FF6800}{ x } \right ) ^ { \color{#FF6800}{ 2 } } \right )$

$ $ If the inside of power is all negative numbers, change them to positive numbers $ $

$\dfrac { 1 } { 2 } \left ( x + y - z \right ) \left ( \left ( x - y \right ) ^ { 2 } + \left ( y + z \right ) ^ { 2 } + \left ( \color{#FF6800}{ z } \color{#FF6800}{ + } \color{#FF6800}{ x } \right ) ^ { \color{#FF6800}{ 2 } } \right )$

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