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Formula
Factorize the expression
$16x ^{ 2 } +16x+4$
$4 \left ( 2 x + 1 \right ) ^ { 2 }$
Arrange the expression in the form of factorization..
$\color{#FF6800}{ 16 } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ 16 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 4 }$
 Use the factoring formula, $a^{2} + 2ab + b^{2} = \left(a+b\right)^{2}$
$\left ( \color{#FF6800}{ 4 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 2 } \right ) ^ { \color{#FF6800}{ 2 } }$
$\left ( \color{#FF6800}{ 4 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 2 } \right ) ^ { 2 }$
 Bind the expressions with the common factor $2$
$\left ( \color{#FF6800}{ 2 } \left ( \color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \right ) \right ) ^ { 2 }$
$\left ( \color{#FF6800}{ 2 } \left ( \color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \right ) \right ) ^ { \color{#FF6800}{ 2 } }$
 Arrange the powers.. 
$\color{#FF6800}{ 2 } ^ { \color{#FF6800}{ 2 } } \left ( \color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \right ) ^ { \color{#FF6800}{ 2 } }$
$\color{#FF6800}{ 2 } ^ { \color{#FF6800}{ 2 } } \left ( \color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \right ) ^ { \color{#FF6800}{ 2 } }$
 Sort the factors 
$\color{#FF6800}{ 4 } \left ( \color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \right ) ^ { \color{#FF6800}{ 2 } }$
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