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Formula
Expand the expression
Factorize the expression
$a ^{ 2 } - \left( b-c \right) ^{ 2 }$
$a ^ { 2 } - b ^ { 2 } + 2 b c - c ^ { 2 }$
Organize polynomials
$a ^ { 2 } - \left ( \color{#FF6800}{ b } \color{#FF6800}{ - } \color{#FF6800}{ c } \right ) ^ { \color{#FF6800}{ 2 } }$
 Expand the binomial expression 
$a ^ { 2 } - \left ( \color{#FF6800}{ b } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ b } \color{#FF6800}{ c } \color{#FF6800}{ + } \color{#FF6800}{ c } ^ { \color{#FF6800}{ 2 } } \right )$
$a ^ { 2 } \color{#FF6800}{ - } \left ( \color{#FF6800}{ b } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ b } \color{#FF6800}{ c } \color{#FF6800}{ + } \color{#FF6800}{ c } ^ { \color{#FF6800}{ 2 } } \right )$
 Change the symbol of each term in parentheses when there is a (-) symbol in front of parentheses 
$a ^ { 2 } \color{#FF6800}{ - } \color{#FF6800}{ b } ^ { \color{#FF6800}{ 2 } } + \color{#FF6800}{ 2 } \color{#FF6800}{ b } \color{#FF6800}{ c } \color{#FF6800}{ - } \color{#FF6800}{ c } ^ { \color{#FF6800}{ 2 } }$
$\left ( a - b + c \right ) \left ( a + b - c \right )$
Arrange the expression in the form of factorization..
$\color{#FF6800}{ a } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \left ( \color{#FF6800}{ b } \color{#FF6800}{ - } \color{#FF6800}{ c } \right ) ^ { \color{#FF6800}{ 2 } }$
 Factorize to use the polynomial formula of sum and difference 
$\left ( \color{#FF6800}{ a } \color{#FF6800}{ + } \color{#FF6800}{ b } \color{#FF6800}{ - } \color{#FF6800}{ c } \right ) \left ( \color{#FF6800}{ a } \color{#FF6800}{ - } \color{#FF6800}{ b } \color{#FF6800}{ + } \color{#FF6800}{ c } \right )$
$\left ( \color{#FF6800}{ a } \color{#FF6800}{ + } \color{#FF6800}{ b } \color{#FF6800}{ - } \color{#FF6800}{ c } \right ) \left ( \color{#FF6800}{ a } \color{#FF6800}{ - } \color{#FF6800}{ b } \color{#FF6800}{ + } \color{#FF6800}{ c } \right )$
 Sort the factors 
$\left ( \color{#FF6800}{ a } \color{#FF6800}{ - } \color{#FF6800}{ b } \color{#FF6800}{ + } \color{#FF6800}{ c } \right ) \left ( \color{#FF6800}{ a } \color{#FF6800}{ + } \color{#FF6800}{ b } \color{#FF6800}{ - } \color{#FF6800}{ c } \right )$
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