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Expand the expression
Answer
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$\left( x+1 \right) \left( x ^{ 2 } +1 \right) \left( x ^{ 4 } +1 \right) \left( x ^{ 8 } +1 \right)$
$x ^ { 15 } + x ^ { 14 } + x ^ { 13 } + x ^ { 12 } + x ^ { 11 } + x ^ { 10 } + x ^ { 9 } + x ^ { 8 } + x ^ { 7 } + x ^ { 6 } + x ^ { 5 } + x ^ { 4 } + x ^ { 3 } + x ^ { 2 } + x + 1$
Organize polynomials
$\left ( \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \right ) \left ( \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \right ) \left ( x ^ { 4 } + 1 \right ) \left ( x ^ { 8 } + 1 \right )$
$ $ Organize the expression with the distributive law $ $
$\left ( \color{#FF6800}{ x } ^ { \color{#FF6800}{ 3 } } \color{#FF6800}{ + } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \right ) \left ( x ^ { 4 } + 1 \right ) \left ( x ^ { 8 } + 1 \right )$
$\left ( \color{#FF6800}{ x } ^ { \color{#FF6800}{ 3 } } \color{#FF6800}{ + } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \right ) \left ( \color{#FF6800}{ x } ^ { \color{#FF6800}{ 4 } } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \right ) \left ( x ^ { 8 } + 1 \right )$
$ $ Organize the expression with the distributive law $ $
$\left ( \color{#FF6800}{ x } ^ { \color{#FF6800}{ 7 } } \color{#FF6800}{ + } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 6 } } \color{#FF6800}{ + } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 5 } } \color{#FF6800}{ + } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 4 } } \color{#FF6800}{ + } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 3 } } \color{#FF6800}{ + } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \right ) \left ( x ^ { 8 } + 1 \right )$
$\left ( \color{#FF6800}{ x } ^ { \color{#FF6800}{ 7 } } \color{#FF6800}{ + } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 6 } } \color{#FF6800}{ + } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 5 } } \color{#FF6800}{ + } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 4 } } \color{#FF6800}{ + } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 3 } } \color{#FF6800}{ + } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \right ) \left ( \color{#FF6800}{ x } ^ { \color{#FF6800}{ 8 } } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \right )$
$ $ Organize the expression with the distributive law $ $
$\color{#FF6800}{ x } ^ { \color{#FF6800}{ 15 } } \color{#FF6800}{ + } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 14 } } \color{#FF6800}{ + } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 13 } } \color{#FF6800}{ + } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 12 } } \color{#FF6800}{ + } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 11 } } \color{#FF6800}{ + } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 10 } } \color{#FF6800}{ + } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 9 } } \color{#FF6800}{ + } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 8 } } \color{#FF6800}{ + } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 7 } } \color{#FF6800}{ + } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 6 } } \color{#FF6800}{ + } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 5 } } \color{#FF6800}{ + } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 4 } } \color{#FF6800}{ + } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 3 } } \color{#FF6800}{ + } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 1 }$
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