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Formula
Expand the expression
$$\left ( a + b + c \right ) \left ( a b + b c + c a \right ) - a b c$$
$a ^ { 2 } b + a ^ { 2 } c + a b ^ { 2 } + 2 a b c + a c ^ { 2 } + b ^ { 2 } c + b c ^ { 2 }$
Organize polynomials
$\left ( a + b + c \right ) \left ( a b + b c + \color{#FF6800}{ c } \color{#FF6800}{ a } \right ) - a b c$
 Sort the order of variables in the mononomial expression 
$\left ( a + b + c \right ) \left ( a b + b c + \color{#FF6800}{ a } \color{#FF6800}{ c } \right ) - a b c$
$\left ( a + b + c \right ) \left ( \color{#FF6800}{ a } \color{#FF6800}{ b } \color{#FF6800}{ + } \color{#FF6800}{ b } \color{#FF6800}{ c } \color{#FF6800}{ + } \color{#FF6800}{ a } \color{#FF6800}{ c } \right ) - a b c$
 Sort the polynomial expressions in descending order 
$\left ( a + b + c \right ) \left ( \color{#FF6800}{ a } \color{#FF6800}{ b } \color{#FF6800}{ + } \color{#FF6800}{ a } \color{#FF6800}{ c } \color{#FF6800}{ + } \color{#FF6800}{ b } \color{#FF6800}{ c } \right ) - a b c$
$\left ( \color{#FF6800}{ a } \color{#FF6800}{ + } \color{#FF6800}{ b } \color{#FF6800}{ + } \color{#FF6800}{ c } \right ) \left ( \color{#FF6800}{ a } \color{#FF6800}{ b } \color{#FF6800}{ + } \color{#FF6800}{ a } \color{#FF6800}{ c } \color{#FF6800}{ + } \color{#FF6800}{ b } \color{#FF6800}{ c } \right ) - a b c$
 Organize the expression with the distributive law 
$\color{#FF6800}{ a } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ b } + \color{#FF6800}{ a } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ c } + \color{#FF6800}{ a } \color{#FF6800}{ b } ^ { \color{#FF6800}{ 2 } } + \color{#FF6800}{ 3 } \color{#FF6800}{ a } \color{#FF6800}{ b } \color{#FF6800}{ c } + \color{#FF6800}{ a } \color{#FF6800}{ c } ^ { \color{#FF6800}{ 2 } } + \color{#FF6800}{ b } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ c } + \color{#FF6800}{ b } \color{#FF6800}{ c } ^ { \color{#FF6800}{ 2 } } - a b c$
$\color{#FF6800}{ a } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ b } \color{#FF6800}{ + } \color{#FF6800}{ a } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ c } \color{#FF6800}{ + } \color{#FF6800}{ a } \color{#FF6800}{ b } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ 3 } \color{#FF6800}{ a } \color{#FF6800}{ b } \color{#FF6800}{ c } \color{#FF6800}{ + } \color{#FF6800}{ a } \color{#FF6800}{ c } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ b } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ c } \color{#FF6800}{ + } \color{#FF6800}{ b } \color{#FF6800}{ c } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ a } \color{#FF6800}{ b } \color{#FF6800}{ c }$
 Organize the similar terms 
$\color{#FF6800}{ a } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ b } \color{#FF6800}{ + } \color{#FF6800}{ a } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ c } \color{#FF6800}{ + } \color{#FF6800}{ a } \color{#FF6800}{ b } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \left ( \color{#FF6800}{ 3 } \color{#FF6800}{ - } \color{#FF6800}{ 1 } \right ) \color{#FF6800}{ a } \color{#FF6800}{ b } \color{#FF6800}{ c } \color{#FF6800}{ + } \color{#FF6800}{ a } \color{#FF6800}{ c } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ b } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ c } \color{#FF6800}{ + } \color{#FF6800}{ b } \color{#FF6800}{ c } ^ { \color{#FF6800}{ 2 } }$
$a ^ { 2 } b + a ^ { 2 } c + a b ^ { 2 } + \left ( \color{#FF6800}{ 3 } \color{#FF6800}{ - } \color{#FF6800}{ 1 } \right ) \color{#FF6800}{ a } \color{#FF6800}{ b } \color{#FF6800}{ c } + a c ^ { 2 } + b ^ { 2 } c + b c ^ { 2 }$
 Arrange the constant term 
$a ^ { 2 } b + a ^ { 2 } c + a b ^ { 2 } + \color{#FF6800}{ 2 } \color{#FF6800}{ a } \color{#FF6800}{ b } \color{#FF6800}{ c } + a c ^ { 2 } + b ^ { 2 } c + b c ^ { 2 }$
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