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Formula
Factorize the expression
$$\left ( a - b \right ) \left ( b - c \right ) \left ( c - a \right )$$
$- \left ( a - b \right ) \left ( a - c \right ) \left ( b - c \right )$
Arrange the expression in the form of factorization..
$\left ( a - b \right ) \left ( b - c \right ) \left ( \color{#FF6800}{ c } \color{#FF6800}{ - } \color{#FF6800}{ a } \right )$
 Organize the expression 
$\left ( a - b \right ) \left ( b - c \right ) \left ( \color{#FF6800}{ - } \color{#FF6800}{ a } \color{#FF6800}{ + } \color{#FF6800}{ c } \right )$
$\left ( a - b \right ) \left ( b - c \right ) \left ( \color{#FF6800}{ - } \color{#FF6800}{ a } \color{#FF6800}{ + } \color{#FF6800}{ c } \right )$
 Bind the expressions with the common factor $- 1$
$\left ( a - b \right ) \left ( b - c \right ) \times \left ( \color{#FF6800}{ - } \left ( \color{#FF6800}{ a } \color{#FF6800}{ - } \color{#FF6800}{ c } \right ) \right )$
$\left ( a - b \right ) \left ( b - c \right ) \times \left ( \color{#FF6800}{ - } \left ( a - c \right ) \right )$
 If you multiply negative numbers by odd numbers, move the (-) sign forward 
$- \left ( a - b \right ) \left ( b - c \right ) \left ( a - c \right )$
$\color{#FF6800}{ - } \left ( \color{#FF6800}{ a } \color{#FF6800}{ - } \color{#FF6800}{ b } \right ) \left ( \color{#FF6800}{ b } \color{#FF6800}{ - } \color{#FF6800}{ c } \right ) \left ( \color{#FF6800}{ a } \color{#FF6800}{ - } \color{#FF6800}{ c } \right )$
 Sort the factors 
$\color{#FF6800}{ - } \left ( \color{#FF6800}{ a } \color{#FF6800}{ - } \color{#FF6800}{ b } \right ) \left ( \color{#FF6800}{ a } \color{#FF6800}{ - } \color{#FF6800}{ c } \right ) \left ( \color{#FF6800}{ b } \color{#FF6800}{ - } \color{#FF6800}{ c } \right )$
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