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Formula
Calculate the value
Factorize by the sum and difference formula
$\left( 2+1 \right) \left( 2 ^{ 2 } +1 \right) \left( 2 ^{ 4 } +1 \right) \left( 2 ^{ 8 } +1 \right)$
$65535$
Calculate the value
$\left ( \color{#FF6800}{ 2 } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \right ) \left ( 2 ^ { 2 } + 1 \right ) \left ( 2 ^ { 4 } + 1 \right ) \left ( 2 ^ { 8 } + 1 \right )$
 Add $2$ and $1$
$\color{#FF6800}{ 3 } \left ( 2 ^ { 2 } + 1 \right ) \left ( 2 ^ { 4 } + 1 \right ) \left ( 2 ^ { 8 } + 1 \right )$
$\color{#FF6800}{ 3 } \left ( \color{#FF6800}{ 2 } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \right ) \left ( \color{#FF6800}{ 2 } ^ { \color{#FF6800}{ 4 } } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \right ) \left ( \color{#FF6800}{ 2 } ^ { \color{#FF6800}{ 8 } } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \right )$
 Expand the expression to calculate the value 
$\color{#FF6800}{ 65535 }$
$2 ^ { 16 } - 1$
Calculation using the sum and difference formula
$\left ( \color{#FF6800}{ 2 } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \right ) \left ( 2 ^ { 2 } + 1 \right ) \left ( 2 ^ { 4 } + 1 \right ) \left ( 2 ^ { 8 } + 1 \right )$
 Multiply $(2-1)$ to the front and $\dfrac{1}{2-1}$ to keep the original expression 
$\color{#FF6800}{ \dfrac { 1 } { 2 - 1 } } \left ( \color{#FF6800}{ 2 } \color{#FF6800}{ - } \color{#FF6800}{ 1 } \right ) \left ( \color{#FF6800}{ 2 } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \right ) \left ( 2 ^ { 2 } + 1 \right ) \left ( 2 ^ { 4 } + 1 \right ) \left ( 2 ^ { 8 } + 1 \right )$
$\dfrac { 1 } { 2 - 1 } \left ( \color{#FF6800}{ 2 } \color{#FF6800}{ - } \color{#FF6800}{ 1 } \right ) \left ( \color{#FF6800}{ 2 } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \right ) \left ( 2 ^ { 2 } + 1 \right ) \left ( 2 ^ { 4 } + 1 \right ) \left ( 2 ^ { 8 } + 1 \right )$
 Expand the expression using $\left(a - b\right)\left(a + b\right) = a^{2} - b^{2}$
$\dfrac { 1 } { 2 - 1 } \left ( \color{#FF6800}{ 2 } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ 1 } ^ { \color{#FF6800}{ 2 } } \right ) \left ( 2 ^ { 2 } + 1 \right ) \left ( 2 ^ { 4 } + 1 \right ) \left ( 2 ^ { 8 } + 1 \right )$
$\dfrac { 1 } { 2 - 1 } \left ( 2 ^ { 2 } - \color{#FF6800}{ 1 } ^ { \color{#FF6800}{ 2 } } \right ) \left ( 2 ^ { 2 } + 1 \right ) \left ( 2 ^ { 4 } + 1 \right ) \left ( 2 ^ { 8 } + 1 \right )$
 Calculate power 
$\dfrac { 1 } { 2 - 1 } \left ( 2 ^ { 2 } - \color{#FF6800}{ 1 } \right ) \left ( 2 ^ { 2 } + 1 \right ) \left ( 2 ^ { 4 } + 1 \right ) \left ( 2 ^ { 8 } + 1 \right )$
$\dfrac { 1 } { 2 - 1 } \left ( \color{#FF6800}{ 2 } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ 1 } \right ) \left ( \color{#FF6800}{ 2 } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \right ) \left ( 2 ^ { 4 } + 1 \right ) \left ( 2 ^ { 8 } + 1 \right )$
 Expand the expression using $\left(a - b\right)\left(a + b\right) = a^{2} - b^{2}$
$\dfrac { 1 } { 2 - 1 } \left ( \left ( \color{#FF6800}{ 2 } ^ { \color{#FF6800}{ 2 } } \right ) ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ 1 } ^ { \color{#FF6800}{ 2 } } \right ) \left ( 2 ^ { 4 } + 1 \right ) \left ( 2 ^ { 8 } + 1 \right )$
$\dfrac { 1 } { 2 - 1 } \left ( \left ( \color{#FF6800}{ 2 } ^ { \color{#FF6800}{ 2 } } \right ) ^ { \color{#FF6800}{ 2 } } - 1 ^ { 2 } \right ) \left ( 2 ^ { 4 } + 1 \right ) \left ( 2 ^ { 8 } + 1 \right )$
 Calculate the power of the power 
$\dfrac { 1 } { 2 - 1 } \left ( \color{#FF6800}{ 2 } ^ { \color{#FF6800}{ 4 } } - 1 ^ { 2 } \right ) \left ( 2 ^ { 4 } + 1 \right ) \left ( 2 ^ { 8 } + 1 \right )$
$\dfrac { 1 } { 2 - 1 } \left ( 2 ^ { 4 } - \color{#FF6800}{ 1 } ^ { \color{#FF6800}{ 2 } } \right ) \left ( 2 ^ { 4 } + 1 \right ) \left ( 2 ^ { 8 } + 1 \right )$
 Calculate power 
$\dfrac { 1 } { 2 - 1 } \left ( 2 ^ { 4 } - \color{#FF6800}{ 1 } \right ) \left ( 2 ^ { 4 } + 1 \right ) \left ( 2 ^ { 8 } + 1 \right )$
$\dfrac { 1 } { 2 - 1 } \left ( \color{#FF6800}{ 2 } ^ { \color{#FF6800}{ 4 } } \color{#FF6800}{ - } \color{#FF6800}{ 1 } \right ) \left ( \color{#FF6800}{ 2 } ^ { \color{#FF6800}{ 4 } } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \right ) \left ( 2 ^ { 8 } + 1 \right )$
 Expand the expression using $\left(a - b\right)\left(a + b\right) = a^{2} - b^{2}$
$\dfrac { 1 } { 2 - 1 } \left ( \left ( \color{#FF6800}{ 2 } ^ { \color{#FF6800}{ 4 } } \right ) ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ 1 } ^ { \color{#FF6800}{ 2 } } \right ) \left ( 2 ^ { 8 } + 1 \right )$
$\dfrac { 1 } { 2 - 1 } \left ( \left ( \color{#FF6800}{ 2 } ^ { \color{#FF6800}{ 4 } } \right ) ^ { \color{#FF6800}{ 2 } } - 1 ^ { 2 } \right ) \left ( 2 ^ { 8 } + 1 \right )$
 Calculate the power of the power 
$\dfrac { 1 } { 2 - 1 } \left ( \color{#FF6800}{ 2 } ^ { \color{#FF6800}{ 8 } } - 1 ^ { 2 } \right ) \left ( 2 ^ { 8 } + 1 \right )$
$\dfrac { 1 } { 2 - 1 } \left ( 2 ^ { 8 } - \color{#FF6800}{ 1 } ^ { \color{#FF6800}{ 2 } } \right ) \left ( 2 ^ { 8 } + 1 \right )$
 Calculate power 
$\dfrac { 1 } { 2 - 1 } \left ( 2 ^ { 8 } - \color{#FF6800}{ 1 } \right ) \left ( 2 ^ { 8 } + 1 \right )$
$\dfrac { 1 } { 2 - 1 } \left ( \color{#FF6800}{ 2 } ^ { \color{#FF6800}{ 8 } } \color{#FF6800}{ - } \color{#FF6800}{ 1 } \right ) \left ( \color{#FF6800}{ 2 } ^ { \color{#FF6800}{ 8 } } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \right )$
 Expand the expression using $\left(a - b\right)\left(a + b\right) = a^{2} - b^{2}$
$\dfrac { 1 } { 2 - 1 } \left ( \left ( \color{#FF6800}{ 2 } ^ { \color{#FF6800}{ 8 } } \right ) ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ 1 } ^ { \color{#FF6800}{ 2 } } \right )$
$\dfrac { 1 } { 2 - 1 } \left ( \left ( \color{#FF6800}{ 2 } ^ { \color{#FF6800}{ 8 } } \right ) ^ { \color{#FF6800}{ 2 } } - 1 ^ { 2 } \right )$
 Calculate the power of the power 
$\dfrac { 1 } { 2 - 1 } \left ( \color{#FF6800}{ 2 } ^ { \color{#FF6800}{ 16 } } - 1 ^ { 2 } \right )$
$\dfrac { 1 } { 2 - 1 } \left ( 2 ^ { 16 } - \color{#FF6800}{ 1 } ^ { \color{#FF6800}{ 2 } } \right )$
 Calculate power 
$\dfrac { 1 } { 2 - 1 } \left ( 2 ^ { 16 } - \color{#FF6800}{ 1 } \right )$
$\dfrac { 1 } { \color{#FF6800}{ 2 } \color{#FF6800}{ - } \color{#FF6800}{ 1 } } \left ( 2 ^ { 16 } - 1 \right )$
 Subtract $1$ from $2$
$\dfrac { 1 } { \color{#FF6800}{ 1 } } \left ( 2 ^ { 16 } - 1 \right )$
$\color{#FF6800}{ \dfrac { 1 } { 1 } } \left ( 2 ^ { 16 } - 1 \right )$
 The denominator and numerator are the same, if being cancelled out, it becomes $1$
$\color{#FF6800}{ 1 } \left ( 2 ^ { 16 } - 1 \right )$
$\color{#FF6800}{ 1 } \left ( 2 ^ { 16 } - 1 \right )$
 Multiplying any number by 1 does not change the value 
$2 ^ { 16 } - 1$
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