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Formula
Factorize the expression
$a ^{ 4 } -1$
$\left ( a - 1 \right ) \left ( a + 1 \right ) \left ( a ^ { 2 } + 1 \right )$
Arrange the expression in the form of factorization..
$\color{#FF6800}{ a } ^ { \color{#FF6800}{ 4 } } \color{#FF6800}{ - } \color{#FF6800}{ 1 }$
 Factorize to use the polynomial formula of sum and difference 
$\left ( \color{#FF6800}{ a } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \right ) \left ( \color{#FF6800}{ a } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \right ) \left ( \color{#FF6800}{ a } \color{#FF6800}{ - } \color{#FF6800}{ 1 } \right )$
$\left ( \color{#FF6800}{ a } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \right ) \left ( \color{#FF6800}{ a } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \right ) \left ( \color{#FF6800}{ a } \color{#FF6800}{ - } \color{#FF6800}{ 1 } \right )$
 Sort the factors 
$\left ( \color{#FF6800}{ a } \color{#FF6800}{ - } \color{#FF6800}{ 1 } \right ) \left ( \color{#FF6800}{ a } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \right ) \left ( \color{#FF6800}{ a } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \right )$
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