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Expand the expression
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Factorize the expression
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Organize equations using specific formulas
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$x ^{ 3 } +8y ^{ 3 } -24xy+64$
$x ^ { 3 } - 24 x y + 8 y ^ { 3 } + 64$
Organize polynomials
$\color{#FF6800}{ x } ^ { \color{#FF6800}{ 3 } } \color{#FF6800}{ + } \color{#FF6800}{ 8 } \color{#FF6800}{ y } ^ { \color{#FF6800}{ 3 } } \color{#FF6800}{ - } \color{#FF6800}{ 24 } \color{#FF6800}{ x } \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ 64 }$
$ $ Sort the polynomial expressions in descending order $ $
$\color{#FF6800}{ x } ^ { \color{#FF6800}{ 3 } } \color{#FF6800}{ - } \color{#FF6800}{ 24 } \color{#FF6800}{ x } \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ 8 } \color{#FF6800}{ y } ^ { \color{#FF6800}{ 3 } } \color{#FF6800}{ + } \color{#FF6800}{ 64 }$
$\left ( x + 2 y + 4 \right ) \left ( x ^ { 2 } - 2 x y - 4 x + 4 y ^ { 2 } - 8 y + 16 \right )$
Arrange the expression in the form of factorization..
$\color{#FF6800}{ x } ^ { \color{#FF6800}{ 3 } } \color{#FF6800}{ + } \color{#FF6800}{ 8 } \color{#FF6800}{ y } ^ { \color{#FF6800}{ 3 } } \color{#FF6800}{ - } \color{#FF6800}{ 24 } \color{#FF6800}{ x } \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ 64 }$
$ $ Arrange an equation using the transformation of the multiplication formula $ $
$\left ( \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 2 } \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ 4 } \right ) \left ( \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ 4 } \color{#FF6800}{ y } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ 4 } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ y } \color{#FF6800}{ - } \color{#FF6800}{ 8 } \color{#FF6800}{ y } \color{#FF6800}{ - } \color{#FF6800}{ 4 } \color{#FF6800}{ x } \right )$
$\left ( x + 2 y + 4 \right ) \left ( \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ 4 } \color{#FF6800}{ y } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ 4 } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ y } \color{#FF6800}{ - } \color{#FF6800}{ 8 } \color{#FF6800}{ y } \color{#FF6800}{ - } \color{#FF6800}{ 4 } \color{#FF6800}{ x } \right )$
$ $ Expand the expression $ $
$\left ( x + 2 y + 4 \right ) \left ( \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ y } \color{#FF6800}{ - } \color{#FF6800}{ 4 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 4 } \color{#FF6800}{ y } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ 8 } \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ 16 } \right )$
$\dfrac { 1 } { 2 } \left ( x + 2 y + 4 \right ) \left ( \left ( x - 2 y \right ) ^ { 2 } + \left ( 2 y - 4 \right ) ^ { 2 } + \left ( 4 - x \right ) ^ { 2 } \right )$
Organize equations using specific formulas
$\color{#FF6800}{ x } ^ { \color{#FF6800}{ 3 } } \color{#FF6800}{ + } \color{#FF6800}{ 8 } \color{#FF6800}{ y } ^ { \color{#FF6800}{ 3 } } \color{#FF6800}{ - } \color{#FF6800}{ 24 } \color{#FF6800}{ x } \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ 64 }$
$ $ Arrange an equation for use of the transformation of the multiplication formula $ $
$\color{#FF6800}{ x } ^ { \color{#FF6800}{ 3 } } \color{#FF6800}{ + } \color{#FF6800}{ 8 } \color{#FF6800}{ y } ^ { \color{#FF6800}{ 3 } } \color{#FF6800}{ + } \color{#FF6800}{ 64 } \color{#FF6800}{ - } \color{#FF6800}{ 24 } \color{#FF6800}{ x } \color{#FF6800}{ y }$
$x ^ { 3 } + \color{#FF6800}{ 8 } \color{#FF6800}{ y } ^ { \color{#FF6800}{ 3 } } + 64 - 24 x y$
$ $ Present as cubic format $ $
$x ^ { 3 } + \left ( \color{#FF6800}{ 2 } \color{#FF6800}{ y } \right ) ^ { \color{#FF6800}{ 3 } } + 64 - 24 x y$
$x ^ { 3 } + \left ( 2 y \right ) ^ { 3 } + \color{#FF6800}{ 64 } - 24 x y$
$ $ Present as cubic format $ $
$x ^ { 3 } + \left ( 2 y \right ) ^ { 3 } + \color{#FF6800}{ 4 } ^ { \color{#FF6800}{ 3 } } - 24 x y$
$\color{#FF6800}{ x } ^ { \color{#FF6800}{ 3 } } \color{#FF6800}{ + } \left ( \color{#FF6800}{ 2 } \color{#FF6800}{ y } \right ) ^ { \color{#FF6800}{ 3 } } \color{#FF6800}{ + } \color{#FF6800}{ 4 } ^ { \color{#FF6800}{ 3 } } \color{#FF6800}{ - } \color{#FF6800}{ 24 } \color{#FF6800}{ x } \color{#FF6800}{ y }$
$ $ Transform into the transformation format of the multiplication formula $ $
$\color{#FF6800}{ x } ^ { \color{#FF6800}{ 3 } } \color{#FF6800}{ + } \left ( \color{#FF6800}{ 2 } \color{#FF6800}{ y } \right ) ^ { \color{#FF6800}{ 3 } } \color{#FF6800}{ + } \color{#FF6800}{ 4 } ^ { \color{#FF6800}{ 3 } } \color{#FF6800}{ - } \color{#FF6800}{ 3 } \color{#FF6800}{ x } \left ( \color{#FF6800}{ 2 } \color{#FF6800}{ y } \right ) \color{#FF6800}{ \times } \color{#FF6800}{ 4 }$
$\color{#FF6800}{ x } ^ { \color{#FF6800}{ 3 } } \color{#FF6800}{ + } \left ( \color{#FF6800}{ 2 } \color{#FF6800}{ y } \right ) ^ { \color{#FF6800}{ 3 } } \color{#FF6800}{ + } \color{#FF6800}{ 4 } ^ { \color{#FF6800}{ 3 } } \color{#FF6800}{ - } \color{#FF6800}{ 3 } \color{#FF6800}{ x } \left ( \color{#FF6800}{ 2 } \color{#FF6800}{ y } \right ) \color{#FF6800}{ \times } \color{#FF6800}{ 4 }$
$ $ Factorize to use $ x^{3}+y^{3}+z^{3}-3xyz=(x+y+z)(x^{2}+y^{2}+z^{2}-xy-yx-zx)$
$\left ( \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 2 } \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ 4 } \right ) \left ( \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \left ( \color{#FF6800}{ 2 } \color{#FF6800}{ y } \right ) ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ 4 } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ x } \left ( \color{#FF6800}{ 2 } \color{#FF6800}{ y } \right ) \color{#FF6800}{ - } \left ( \color{#FF6800}{ 2 } \color{#FF6800}{ y } \right ) \color{#FF6800}{ \times } \color{#FF6800}{ 4 } \color{#FF6800}{ - } \color{#FF6800}{ x } \color{#FF6800}{ \times } \color{#FF6800}{ 4 } \right )$
$\left ( x + 2 y + 4 \right ) \left ( \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \left ( \color{#FF6800}{ 2 } \color{#FF6800}{ y } \right ) ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ 4 } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ x } \left ( \color{#FF6800}{ 2 } \color{#FF6800}{ y } \right ) \color{#FF6800}{ - } \left ( \color{#FF6800}{ 2 } \color{#FF6800}{ y } \right ) \color{#FF6800}{ \times } \color{#FF6800}{ 4 } \color{#FF6800}{ - } \color{#FF6800}{ x } \color{#FF6800}{ \times } \color{#FF6800}{ 4 } \right )$
$ $ Organize equations using specific formulas $ $
$\left ( x + 2 y + 4 \right ) \times \color{#FF6800}{ \dfrac { 1 } { 2 } } \left ( \left ( \color{#FF6800}{ x } \color{#FF6800}{ - } \left ( \color{#FF6800}{ 2 } \color{#FF6800}{ y } \right ) \right ) ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \left ( \color{#FF6800}{ 2 } \color{#FF6800}{ y } \color{#FF6800}{ - } \color{#FF6800}{ 4 } \right ) ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \left ( \color{#FF6800}{ 4 } \color{#FF6800}{ - } \color{#FF6800}{ x } \right ) ^ { \color{#FF6800}{ 2 } } \right )$
$\left ( \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 2 } \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ 4 } \right ) \color{#FF6800}{ \times } \color{#FF6800}{ \dfrac { 1 } { 2 } } \left ( \left ( \color{#FF6800}{ x } \color{#FF6800}{ - } \left ( \color{#FF6800}{ 2 } \color{#FF6800}{ y } \right ) \right ) ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \left ( \color{#FF6800}{ 2 } \color{#FF6800}{ y } \color{#FF6800}{ - } \color{#FF6800}{ 4 } \right ) ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \left ( \color{#FF6800}{ 4 } \color{#FF6800}{ - } \color{#FF6800}{ x } \right ) ^ { \color{#FF6800}{ 2 } } \right )$
$ $ Organize the expression $ $
$\color{#FF6800}{ \dfrac { 1 } { 2 } } \left ( \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 2 } \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ 4 } \right ) \left ( \left ( \color{#FF6800}{ x } \color{#FF6800}{ - } \left ( \color{#FF6800}{ 2 } \color{#FF6800}{ y } \right ) \right ) ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \left ( \color{#FF6800}{ 2 } \color{#FF6800}{ y } \color{#FF6800}{ - } \color{#FF6800}{ 4 } \right ) ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \left ( \color{#FF6800}{ 4 } \color{#FF6800}{ - } \color{#FF6800}{ x } \right ) ^ { \color{#FF6800}{ 2 } } \right )$
$\dfrac { 1 } { 2 } \left ( x + 2 y + 4 \right ) \left ( \left ( x \color{#FF6800}{ - } \left ( \color{#FF6800}{ 2 } \color{#FF6800}{ y } \right ) \right ) ^ { 2 } + \left ( 2 y - 4 \right ) ^ { 2 } + \left ( 4 - x \right ) ^ { 2 } \right )$
$ $ Get rid of unnecessary parentheses $ $
$\dfrac { 1 } { 2 } \left ( x + 2 y + 4 \right ) \left ( \left ( x \color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ y } \right ) ^ { 2 } + \left ( 2 y - 4 \right ) ^ { 2 } + \left ( 4 - x \right ) ^ { 2 } \right )$
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