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Factorize the expression
$2x ^{ 2 } +4xy+2y ^{ 2 }$
$2 \left ( x + y \right ) ^ { 2 }$
Arrange the expression in the form of factorization..
$\color{#FF6800}{ 2 } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ 4 } \color{#FF6800}{ x } \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ 2 } \color{#FF6800}{ y } ^ { \color{#FF6800}{ 2 } }$
 Tie a common factor 
$\color{#FF6800}{ 2 } \left ( \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ y } ^ { \color{#FF6800}{ 2 } } \right )$
$2 \left ( \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ y } ^ { \color{#FF6800}{ 2 } } \right )$
 Use the factoring formula, $a^{2} + 2ab + b^{2} = \left(a+b\right)^{2}$
$2 \left ( \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ y } \right ) ^ { \color{#FF6800}{ 2 } }$
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