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Formula
Factorize the expression
$4a ^{ 2 } -4b ^{ 2 } +4b-1$
$\left ( 2 a - 2 b + 1 \right ) \left ( 2 a + 2 b - 1 \right )$
Arrange the expression in the form of factorization..
$\color{#FF6800}{ 4 } \color{#FF6800}{ a } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ 4 } \color{#FF6800}{ b } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ 4 } \color{#FF6800}{ b } \color{#FF6800}{ - } \color{#FF6800}{ 1 }$
 Factorize to use perfect square expression, and the sum and difference formula 
$\left ( \color{#FF6800}{ 2 } \color{#FF6800}{ a } \color{#FF6800}{ + } \color{#FF6800}{ 2 } \color{#FF6800}{ b } \color{#FF6800}{ - } \color{#FF6800}{ 1 } \right ) \left ( \color{#FF6800}{ 2 } \color{#FF6800}{ a } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ b } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \right )$
$\left ( \color{#FF6800}{ 2 } \color{#FF6800}{ a } \color{#FF6800}{ + } \color{#FF6800}{ 2 } \color{#FF6800}{ b } \color{#FF6800}{ - } \color{#FF6800}{ 1 } \right ) \left ( \color{#FF6800}{ 2 } \color{#FF6800}{ a } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ b } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \right )$
 Sort the factors 
$\left ( \color{#FF6800}{ 2 } \color{#FF6800}{ a } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ b } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \right ) \left ( \color{#FF6800}{ 2 } \color{#FF6800}{ a } \color{#FF6800}{ + } \color{#FF6800}{ 2 } \color{#FF6800}{ b } \color{#FF6800}{ - } \color{#FF6800}{ 1 } \right )$
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