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Formula
Factorize the expression
$-2x ^{ 2 } +50$
$- 2 \left ( x - 5 \right ) \left ( x + 5 \right )$
Arrange the expression in the form of factorization..
$\color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ 50 }$
 Factorize to use the polynomial formula of sum and difference 
$\color{#FF6800}{ 2 } \left ( \color{#FF6800}{ 5 } \color{#FF6800}{ + } \color{#FF6800}{ x } \right ) \left ( \color{#FF6800}{ 5 } \color{#FF6800}{ - } \color{#FF6800}{ x } \right )$
$2 \left ( \color{#FF6800}{ 5 } \color{#FF6800}{ + } \color{#FF6800}{ x } \right ) \left ( 5 - x \right )$
 Organize the expression 
$2 \left ( \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 5 } \right ) \left ( 5 - x \right )$
$2 \left ( x + 5 \right ) \left ( \color{#FF6800}{ 5 } \color{#FF6800}{ - } \color{#FF6800}{ x } \right )$
 Expand the expression 
$2 \left ( x + 5 \right ) \left ( \color{#FF6800}{ - } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 5 } \right )$
$2 \left ( x + 5 \right ) \left ( \color{#FF6800}{ - } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 5 } \right )$
 Bind the expressions with the common factor $- 1$
$2 \left ( x + 5 \right ) \times \left ( \color{#FF6800}{ - } \left ( \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 5 } \right ) \right )$
$2 \left ( x + 5 \right ) \times \left ( \color{#FF6800}{ - } \left ( x - 5 \right ) \right )$
 If you multiply negative numbers by odd numbers, move the (-) sign forward 
$- 2 \left ( x + 5 \right ) \left ( x - 5 \right )$
$\color{#FF6800}{ - } \color{#FF6800}{ 2 } \left ( \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 5 } \right ) \left ( \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 5 } \right )$
 Sort the factors 
$\color{#FF6800}{ - } \color{#FF6800}{ 2 } \left ( \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 5 } \right ) \left ( \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 5 } \right )$
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