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Formula
Factorize the expression
$-x ^{ 2 } +y ^{ 2 }$
$- \left ( x - y \right ) \left ( x + y \right )$
Arrange the expression in the form of factorization..
$\color{#FF6800}{ - } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ y } ^ { \color{#FF6800}{ 2 } }$
 Factorize to use the polynomial formula of sum and difference 
$\left ( \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ x } \right ) \left ( \color{#FF6800}{ y } \color{#FF6800}{ - } \color{#FF6800}{ x } \right )$
$\left ( \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ x } \right ) \left ( y - x \right )$
 Organize the expression 
$\left ( \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ y } \right ) \left ( y - x \right )$
$\left ( x + y \right ) \left ( \color{#FF6800}{ y } \color{#FF6800}{ - } \color{#FF6800}{ x } \right )$
 Organize the expression 
$\left ( x + y \right ) \left ( \color{#FF6800}{ - } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ y } \right )$
$\left ( x + y \right ) \left ( \color{#FF6800}{ - } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ y } \right )$
 Bind the expressions with the common factor $- 1$
$\left ( x + y \right ) \times \left ( \color{#FF6800}{ - } \left ( \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ y } \right ) \right )$
$\left ( \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ y } \right ) \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \left ( \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ y } \right ) \right )$
 Sort the factors 
$\color{#FF6800}{ - } \left ( \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ y } \right ) \left ( \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ y } \right )$
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