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Formula
Factorize the expression
$100z ^{ 2 } -100z+25$
$25 \left ( 2 z - 1 \right ) ^ { 2 }$
Arrange the expression in the form of factorization..
$\color{#FF6800}{ 100 } \color{#FF6800}{ z } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ 100 } \color{#FF6800}{ z } \color{#FF6800}{ + } \color{#FF6800}{ 25 }$
 Use the factoring formula, $a^{2}-2ab + b^{2} = \left(a-b\right)^{2}$
$\left ( \color{#FF6800}{ 10 } \color{#FF6800}{ z } \color{#FF6800}{ - } \color{#FF6800}{ 5 } \right ) ^ { \color{#FF6800}{ 2 } }$
$\left ( \color{#FF6800}{ 10 } \color{#FF6800}{ z } \color{#FF6800}{ - } \color{#FF6800}{ 5 } \right ) ^ { 2 }$
 Bind the expressions with the common factor $5$
$\left ( \color{#FF6800}{ 5 } \left ( \color{#FF6800}{ 2 } \color{#FF6800}{ z } \color{#FF6800}{ - } \color{#FF6800}{ 1 } \right ) \right ) ^ { 2 }$
$\left ( \color{#FF6800}{ 5 } \left ( \color{#FF6800}{ 2 } \color{#FF6800}{ z } \color{#FF6800}{ - } \color{#FF6800}{ 1 } \right ) \right ) ^ { \color{#FF6800}{ 2 } }$
 Arrange the powers.. 
$\color{#FF6800}{ 5 } ^ { \color{#FF6800}{ 2 } } \left ( \color{#FF6800}{ 2 } \color{#FF6800}{ z } \color{#FF6800}{ - } \color{#FF6800}{ 1 } \right ) ^ { \color{#FF6800}{ 2 } }$
$\color{#FF6800}{ 5 } ^ { \color{#FF6800}{ 2 } } \left ( \color{#FF6800}{ 2 } \color{#FF6800}{ z } \color{#FF6800}{ - } \color{#FF6800}{ 1 } \right ) ^ { \color{#FF6800}{ 2 } }$
 Sort the factors 
$\color{#FF6800}{ 25 } \left ( \color{#FF6800}{ 2 } \color{#FF6800}{ z } \color{#FF6800}{ - } \color{#FF6800}{ 1 } \right ) ^ { \color{#FF6800}{ 2 } }$
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