# Calculator search results

Formula
Factorize the expression
$x ^{ 19 } -x ^{ 9 }$
$x ^ { 9 } \left ( x - 1 \right ) \left ( x + 1 \right ) \left ( x ^ { 4 } - x ^ { 3 } + x ^ { 2 } - x + 1 \right ) \left ( x ^ { 4 } + x ^ { 3 } + x ^ { 2 } + x + 1 \right )$
Arrange the expression in the form of factorization..
$\color{#FF6800}{ x } ^ { \color{#FF6800}{ 19 } } \color{#FF6800}{ - } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 9 } }$
 Factorize to use the polynomial formula of sum and difference 
$\color{#FF6800}{ x } ^ { \color{#FF6800}{ 9 } } \left ( \color{#FF6800}{ x } ^ { \color{#FF6800}{ 5 } } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \right ) \left ( \color{#FF6800}{ x } ^ { \color{#FF6800}{ 5 } } \color{#FF6800}{ - } \color{#FF6800}{ 1 } \right )$
$x ^ { 9 } \left ( \color{#FF6800}{ x } ^ { \color{#FF6800}{ 5 } } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \right ) \left ( x ^ { 5 } - 1 \right )$
 Do factorization 
$x ^ { 9 } \left ( \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \right ) \left ( \color{#FF6800}{ x } ^ { \color{#FF6800}{ 4 } } \color{#FF6800}{ - } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 3 } } \color{#FF6800}{ + } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \right ) \left ( x ^ { 5 } - 1 \right )$
$x ^ { 9 } \left ( x + 1 \right ) \left ( x ^ { 4 } - x ^ { 3 } + x ^ { 2 } - x + 1 \right ) \left ( \color{#FF6800}{ x } ^ { \color{#FF6800}{ 5 } } \color{#FF6800}{ - } \color{#FF6800}{ 1 } \right )$
 Do factorization 
$x ^ { 9 } \left ( x + 1 \right ) \left ( x ^ { 4 } - x ^ { 3 } + x ^ { 2 } - x + 1 \right ) \left ( \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 1 } \right ) \left ( \color{#FF6800}{ x } ^ { \color{#FF6800}{ 4 } } \color{#FF6800}{ + } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 3 } } \color{#FF6800}{ + } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \right )$
$\color{#FF6800}{ x } ^ { \color{#FF6800}{ 9 } } \left ( \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \right ) \left ( \color{#FF6800}{ x } ^ { \color{#FF6800}{ 4 } } \color{#FF6800}{ - } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 3 } } \color{#FF6800}{ + } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \right ) \left ( \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 1 } \right ) \left ( \color{#FF6800}{ x } ^ { \color{#FF6800}{ 4 } } \color{#FF6800}{ + } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 3 } } \color{#FF6800}{ + } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \right )$
 Sort the factors 
$\color{#FF6800}{ x } ^ { \color{#FF6800}{ 9 } } \left ( \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 1 } \right ) \left ( \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \right ) \left ( \color{#FF6800}{ x } ^ { \color{#FF6800}{ 4 } } \color{#FF6800}{ - } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 3 } } \color{#FF6800}{ + } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \right ) \left ( \color{#FF6800}{ x } ^ { \color{#FF6800}{ 4 } } \color{#FF6800}{ + } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 3 } } \color{#FF6800}{ + } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \right )$
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