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Factorize by the sum and difference formula
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$65535$
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 $ $
$\color{#FF6800}{ \dfrac { \color{#FF6800}{ 1 } } { \color{#FF6800}{ 2 } \color{#FF6800}{ - } \color{#FF6800}{ 1 } } } \left ( \color{#FF6800}{ 2 } \color{#FF6800}{ - } \color{#FF6800}{ 1 } \right ) \left ( \color{#FF6800}{ 2 } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \right ) \left ( 2 ^ { 2 } + 1 \right ) \left ( 2 ^ { 4 } + 1 \right ) \left ( 2 ^ { 8 } + 1 \right )$
$\dfrac { 1 } { 2 - 1 } \left ( \color{#FF6800}{ 2 } \color{#FF6800}{ - } \color{#FF6800}{ 1 } \right ) \left ( \color{#FF6800}{ 2 } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \right ) \left ( 2 ^ { 2 } + 1 \right ) \left ( 2 ^ { 4 } + 1 \right ) \left ( 2 ^ { 8 } + 1 \right )$
$ $ 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$
$\dfrac { 1 } { \color{#FF6800}{ 1 } } \left ( 2 ^ { 16 } - 1 \right )$
$\color{#FF6800}{ \dfrac { \color{#FF6800}{ 1 } } { \color{#FF6800}{ 1 } } } \left ( 2 ^ { 16 } - 1 \right )$
$ $ 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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