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Expand the expression
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Factorize the expression
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$\left( 1-a ^{ 4 } \right) \left( 1+a ^{ 4 } \right)$
$- a ^ { 8 } + 1$
Organize polynomials
$\left ( \color{#FF6800}{ 1 } \color{#FF6800}{ - } \color{#FF6800}{ a } ^ { \color{#FF6800}{ 4 } } \right ) \left ( 1 + a ^ { 4 } \right )$
$ $ Sort the polynomial expressions in descending order $ $
$\left ( \color{#FF6800}{ - } \color{#FF6800}{ a } ^ { \color{#FF6800}{ 4 } } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \right ) \left ( 1 + a ^ { 4 } \right )$
$\left ( - a ^ { 4 } + 1 \right ) \left ( \color{#FF6800}{ 1 } \color{#FF6800}{ + } \color{#FF6800}{ a } ^ { \color{#FF6800}{ 4 } } \right )$
$ $ Sort the polynomial expressions in descending order $ $
$\left ( - a ^ { 4 } + 1 \right ) \left ( \color{#FF6800}{ a } ^ { \color{#FF6800}{ 4 } } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \right )$
$\left ( \color{#FF6800}{ - } \color{#FF6800}{ a } ^ { \color{#FF6800}{ 4 } } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \right ) \left ( \color{#FF6800}{ a } ^ { \color{#FF6800}{ 4 } } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \right )$
$ $ Organize the expression with the distributive law $ $
$\color{#FF6800}{ - } \color{#FF6800}{ a } ^ { \color{#FF6800}{ 8 } } \color{#FF6800}{ + } \color{#FF6800}{ 1 }$
$- \left ( a - 1 \right ) \left ( a + 1 \right ) \left ( a ^ { 2 } + 1 \right ) \left ( a ^ { 4 } + 1 \right )$
Arrange the expression in the form of factorization..
$\left ( \color{#FF6800}{ 1 } \color{#FF6800}{ - } \color{#FF6800}{ a } ^ { \color{#FF6800}{ 4 } } \right ) \left ( 1 + a ^ { 4 } \right )$
$ $ Factorize to use the polynomial formula of sum and difference $ $
$\left ( \color{#FF6800}{ 1 } \color{#FF6800}{ + } \color{#FF6800}{ a } ^ { \color{#FF6800}{ 2 } } \right ) \left ( \color{#FF6800}{ 1 } \color{#FF6800}{ + } \color{#FF6800}{ a } \right ) \left ( \color{#FF6800}{ 1 } \color{#FF6800}{ - } \color{#FF6800}{ a } \right ) \left ( 1 + a ^ { 4 } \right )$
$\left ( \color{#FF6800}{ 1 } \color{#FF6800}{ + } \color{#FF6800}{ a } ^ { \color{#FF6800}{ 2 } } \right ) \left ( 1 + a \right ) \left ( 1 - a \right ) \left ( 1 + a ^ { 4 } \right )$
$ $ Organize the expression $ $
$\left ( \color{#FF6800}{ a } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \right ) \left ( 1 + a \right ) \left ( 1 - a \right ) \left ( 1 + a ^ { 4 } \right )$
$\left ( a ^ { 2 } + 1 \right ) \left ( \color{#FF6800}{ 1 } \color{#FF6800}{ + } \color{#FF6800}{ a } \right ) \left ( 1 - a \right ) \left ( 1 + a ^ { 4 } \right )$
$ $ Organize the expression $ $
$\left ( a ^ { 2 } + 1 \right ) \left ( \color{#FF6800}{ a } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \right ) \left ( 1 - a \right ) \left ( 1 + a ^ { 4 } \right )$
$\left ( a ^ { 2 } + 1 \right ) \left ( a + 1 \right ) \left ( \color{#FF6800}{ 1 } \color{#FF6800}{ - } \color{#FF6800}{ a } \right ) \left ( 1 + a ^ { 4 } \right )$
$ $ Expand the expression $ $
$\left ( a ^ { 2 } + 1 \right ) \left ( a + 1 \right ) \left ( \color{#FF6800}{ - } \color{#FF6800}{ a } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \right ) \left ( 1 + a ^ { 4 } \right )$
$\left ( a ^ { 2 } + 1 \right ) \left ( a + 1 \right ) \left ( \color{#FF6800}{ - } \color{#FF6800}{ a } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \right ) \left ( 1 + a ^ { 4 } \right )$
$ $ Bind the expressions with the common factor $ - 1$
$\left ( a ^ { 2 } + 1 \right ) \left ( a + 1 \right ) \times \left ( \color{#FF6800}{ - } \left ( \color{#FF6800}{ a } \color{#FF6800}{ - } \color{#FF6800}{ 1 } \right ) \right ) \left ( 1 + a ^ { 4 } \right )$
$\left ( a ^ { 2 } + 1 \right ) \left ( a + 1 \right ) \times \left ( \color{#FF6800}{ - } \left ( a - 1 \right ) \right ) \left ( 1 + a ^ { 4 } \right )$
$ $ If you multiply negative numbers by odd numbers, move the (-) sign forward $ $
$- \left ( a ^ { 2 } + 1 \right ) \left ( a + 1 \right ) \left ( a - 1 \right ) \left ( 1 + a ^ { 4 } \right )$
$\color{#FF6800}{ - } \left ( \color{#FF6800}{ a } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \right ) \left ( \color{#FF6800}{ a } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \right ) \left ( \color{#FF6800}{ a } \color{#FF6800}{ - } \color{#FF6800}{ 1 } \right ) \left ( 1 + a ^ { 4 } \right )$
$ $ Sort the factors $ $
$\color{#FF6800}{ - } \left ( \color{#FF6800}{ a } \color{#FF6800}{ - } \color{#FF6800}{ 1 } \right ) \left ( \color{#FF6800}{ a } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \right ) \left ( \color{#FF6800}{ a } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \right ) \left ( 1 + a ^ { 4 } \right )$
$- \left ( a - 1 \right ) \left ( a + 1 \right ) \left ( a ^ { 2 } + 1 \right ) \left ( \color{#FF6800}{ 1 } \color{#FF6800}{ + } \color{#FF6800}{ a } ^ { \color{#FF6800}{ 4 } } \right )$
$ $ Organize the expression $ $
$- \left ( a - 1 \right ) \left ( a + 1 \right ) \left ( a ^ { 2 } + 1 \right ) \left ( \color{#FF6800}{ a } ^ { \color{#FF6800}{ 4 } } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \right )$
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