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Formula
Calculate the value
Factorize by the sum and difference formula
$\left( 5+1 \right) \left( 5 ^{ 2 } +1 \right) \left( 5 ^{ 4 } +1 \right) \left( 5 ^{ 8 } +1 \right)$
$38146972656$
Calculate the value
$\left ( \color{#FF6800}{ 5 } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \right ) \left ( 5 ^ { 2 } + 1 \right ) \left ( 5 ^ { 4 } + 1 \right ) \left ( 5 ^ { 8 } + 1 \right )$
 Add $5$ and $1$
$\color{#FF6800}{ 6 } \left ( 5 ^ { 2 } + 1 \right ) \left ( 5 ^ { 4 } + 1 \right ) \left ( 5 ^ { 8 } + 1 \right )$
$\color{#FF6800}{ 6 } \left ( \color{#FF6800}{ 5 } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \right ) \left ( \color{#FF6800}{ 5 } ^ { \color{#FF6800}{ 4 } } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \right ) \left ( \color{#FF6800}{ 5 } ^ { \color{#FF6800}{ 8 } } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \right )$
 Expand the expression to calculate the value 
$\color{#FF6800}{ 38146972656 }$
$\dfrac { 1 } { 4 } \left ( 5 ^ { 16 } - 1 \right )$
Calculation using the sum and difference formula
$\left ( \color{#FF6800}{ 5 } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \right ) \left ( 5 ^ { 2 } + 1 \right ) \left ( 5 ^ { 4 } + 1 \right ) \left ( 5 ^ { 8 } + 1 \right )$
 Multiply $(5-1)$ to the front and $\dfrac{1}{5-1}$ to keep the original expression 
$\color{#FF6800}{ \dfrac { 1 } { 5 - 1 } } \left ( \color{#FF6800}{ 5 } \color{#FF6800}{ - } \color{#FF6800}{ 1 } \right ) \left ( \color{#FF6800}{ 5 } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \right ) \left ( 5 ^ { 2 } + 1 \right ) \left ( 5 ^ { 4 } + 1 \right ) \left ( 5 ^ { 8 } + 1 \right )$
$\dfrac { 1 } { 5 - 1 } \left ( \color{#FF6800}{ 5 } \color{#FF6800}{ - } \color{#FF6800}{ 1 } \right ) \left ( \color{#FF6800}{ 5 } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \right ) \left ( 5 ^ { 2 } + 1 \right ) \left ( 5 ^ { 4 } + 1 \right ) \left ( 5 ^ { 8 } + 1 \right )$
 Expand the expression using $\left(a - b\right)\left(a + b\right) = a^{2} - b^{2}$
$\dfrac { 1 } { 5 - 1 } \left ( \color{#FF6800}{ 5 } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ 1 } ^ { \color{#FF6800}{ 2 } } \right ) \left ( 5 ^ { 2 } + 1 \right ) \left ( 5 ^ { 4 } + 1 \right ) \left ( 5 ^ { 8 } + 1 \right )$
$\dfrac { 1 } { 5 - 1 } \left ( 5 ^ { 2 } - \color{#FF6800}{ 1 } ^ { \color{#FF6800}{ 2 } } \right ) \left ( 5 ^ { 2 } + 1 \right ) \left ( 5 ^ { 4 } + 1 \right ) \left ( 5 ^ { 8 } + 1 \right )$
 Calculate power 
$\dfrac { 1 } { 5 - 1 } \left ( 5 ^ { 2 } - \color{#FF6800}{ 1 } \right ) \left ( 5 ^ { 2 } + 1 \right ) \left ( 5 ^ { 4 } + 1 \right ) \left ( 5 ^ { 8 } + 1 \right )$
$\dfrac { 1 } { 5 - 1 } \left ( \color{#FF6800}{ 5 } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ 1 } \right ) \left ( \color{#FF6800}{ 5 } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \right ) \left ( 5 ^ { 4 } + 1 \right ) \left ( 5 ^ { 8 } + 1 \right )$
 Expand the expression using $\left(a - b\right)\left(a + b\right) = a^{2} - b^{2}$
$\dfrac { 1 } { 5 - 1 } \left ( \left ( \color{#FF6800}{ 5 } ^ { \color{#FF6800}{ 2 } } \right ) ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ 1 } ^ { \color{#FF6800}{ 2 } } \right ) \left ( 5 ^ { 4 } + 1 \right ) \left ( 5 ^ { 8 } + 1 \right )$
$\dfrac { 1 } { 5 - 1 } \left ( \left ( \color{#FF6800}{ 5 } ^ { \color{#FF6800}{ 2 } } \right ) ^ { \color{#FF6800}{ 2 } } - 1 ^ { 2 } \right ) \left ( 5 ^ { 4 } + 1 \right ) \left ( 5 ^ { 8 } + 1 \right )$
 Calculate the power of the power 
$\dfrac { 1 } { 5 - 1 } \left ( \color{#FF6800}{ 5 } ^ { \color{#FF6800}{ 4 } } - 1 ^ { 2 } \right ) \left ( 5 ^ { 4 } + 1 \right ) \left ( 5 ^ { 8 } + 1 \right )$
$\dfrac { 1 } { 5 - 1 } \left ( 5 ^ { 4 } - \color{#FF6800}{ 1 } ^ { \color{#FF6800}{ 2 } } \right ) \left ( 5 ^ { 4 } + 1 \right ) \left ( 5 ^ { 8 } + 1 \right )$
 Calculate power 
$\dfrac { 1 } { 5 - 1 } \left ( 5 ^ { 4 } - \color{#FF6800}{ 1 } \right ) \left ( 5 ^ { 4 } + 1 \right ) \left ( 5 ^ { 8 } + 1 \right )$
$\dfrac { 1 } { 5 - 1 } \left ( \color{#FF6800}{ 5 } ^ { \color{#FF6800}{ 4 } } \color{#FF6800}{ - } \color{#FF6800}{ 1 } \right ) \left ( \color{#FF6800}{ 5 } ^ { \color{#FF6800}{ 4 } } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \right ) \left ( 5 ^ { 8 } + 1 \right )$
 Expand the expression using $\left(a - b\right)\left(a + b\right) = a^{2} - b^{2}$
$\dfrac { 1 } { 5 - 1 } \left ( \left ( \color{#FF6800}{ 5 } ^ { \color{#FF6800}{ 4 } } \right ) ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ 1 } ^ { \color{#FF6800}{ 2 } } \right ) \left ( 5 ^ { 8 } + 1 \right )$
$\dfrac { 1 } { 5 - 1 } \left ( \left ( \color{#FF6800}{ 5 } ^ { \color{#FF6800}{ 4 } } \right ) ^ { \color{#FF6800}{ 2 } } - 1 ^ { 2 } \right ) \left ( 5 ^ { 8 } + 1 \right )$
 Calculate the power of the power 
$\dfrac { 1 } { 5 - 1 } \left ( \color{#FF6800}{ 5 } ^ { \color{#FF6800}{ 8 } } - 1 ^ { 2 } \right ) \left ( 5 ^ { 8 } + 1 \right )$
$\dfrac { 1 } { 5 - 1 } \left ( 5 ^ { 8 } - \color{#FF6800}{ 1 } ^ { \color{#FF6800}{ 2 } } \right ) \left ( 5 ^ { 8 } + 1 \right )$
 Calculate power 
$\dfrac { 1 } { 5 - 1 } \left ( 5 ^ { 8 } - \color{#FF6800}{ 1 } \right ) \left ( 5 ^ { 8 } + 1 \right )$
$\dfrac { 1 } { 5 - 1 } \left ( \color{#FF6800}{ 5 } ^ { \color{#FF6800}{ 8 } } \color{#FF6800}{ - } \color{#FF6800}{ 1 } \right ) \left ( \color{#FF6800}{ 5 } ^ { \color{#FF6800}{ 8 } } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \right )$
 Expand the expression using $\left(a - b\right)\left(a + b\right) = a^{2} - b^{2}$
$\dfrac { 1 } { 5 - 1 } \left ( \left ( \color{#FF6800}{ 5 } ^ { \color{#FF6800}{ 8 } } \right ) ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ 1 } ^ { \color{#FF6800}{ 2 } } \right )$
$\dfrac { 1 } { 5 - 1 } \left ( \left ( \color{#FF6800}{ 5 } ^ { \color{#FF6800}{ 8 } } \right ) ^ { \color{#FF6800}{ 2 } } - 1 ^ { 2 } \right )$
 Calculate the power of the power 
$\dfrac { 1 } { 5 - 1 } \left ( \color{#FF6800}{ 5 } ^ { \color{#FF6800}{ 16 } } - 1 ^ { 2 } \right )$
$\dfrac { 1 } { 5 - 1 } \left ( 5 ^ { 16 } - \color{#FF6800}{ 1 } ^ { \color{#FF6800}{ 2 } } \right )$
 Calculate power 
$\dfrac { 1 } { 5 - 1 } \left ( 5 ^ { 16 } - \color{#FF6800}{ 1 } \right )$
$\dfrac { 1 } { \color{#FF6800}{ 5 } \color{#FF6800}{ - } \color{#FF6800}{ 1 } } \left ( 5 ^ { 16 } - 1 \right )$
 Subtract $1$ from $5$
$\dfrac { 1 } { \color{#FF6800}{ 4 } } \left ( 5 ^ { 16 } - 1 \right )$
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