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Formula
Calculate the value
Factorize by the perfect square formula
$y ^{ 2 } - \dfrac{ 2 }{ 3 } y+ \dfrac{ 1 }{ 9 }$
$\dfrac { 9 y ^ { 2 } - 6 y + 1 } { 9 }$
Arrange the rational expression
$\color{#FF6800}{ y } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 2 } { 3 } } \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ \dfrac { 1 } { 9 } }$
 Calculate the expression as a fraction format 
$\color{#FF6800}{ \dfrac { 9 y ^ { 2 } - 6 y + 1 } { 9 } }$
$\dfrac { 1 } { 9 } \left ( 3 y - 1 \right ) ^ { 2 }$
Express as the perfect square formula
$\color{#FF6800}{ y } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 2 } { 3 } } \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ \dfrac { 1 } { 9 } }$
 Bind the expressions with the common factor $\dfrac { 1 } { 9 }$
$\color{#FF6800}{ \dfrac { 1 } { 9 } } \left ( \color{#FF6800}{ 9 } \color{#FF6800}{ y } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ 6 } \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \right )$
$\dfrac { 1 } { 9 } \left ( \color{#FF6800}{ 9 } \color{#FF6800}{ y } ^ { \color{#FF6800}{ 2 } } - 6 y + 1 \right )$
 Present as the shape of the power 
$\dfrac { 1 } { 9 } \left ( \color{#FF6800}{ 3 } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ y } ^ { \color{#FF6800}{ 2 } } - 6 y + 1 \right )$
$\dfrac { 1 } { 9 } \left ( \color{#FF6800}{ 3 } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ y } ^ { \color{#FF6800}{ 2 } } - 6 y + 1 \right )$
 Binding the power 
$\dfrac { 1 } { 9 } \left ( \left ( \color{#FF6800}{ 3 } \color{#FF6800}{ y } \right ) ^ { \color{#FF6800}{ 2 } } - 6 y + 1 \right )$
$\dfrac { 1 } { 9 } \left ( \left ( 3 y \right ) ^ { 2 } - 6 y + \color{#FF6800}{ 1 } \right )$
 Present as the shape of the power 
$\dfrac { 1 } { 9 } \left ( \left ( 3 y \right ) ^ { 2 } - 6 y + \color{#FF6800}{ 1 } ^ { \color{#FF6800}{ 2 } } \right )$
$\dfrac { 1 } { 9 } \left ( \left ( 3 y \right ) ^ { 2 } \color{#FF6800}{ - } \color{#FF6800}{ 6 } \color{#FF6800}{ y } + 1 ^ { 2 } \right )$
 Change the term in the middle 
$\dfrac { 1 } { 9 } \left ( \left ( 3 y \right ) ^ { 2 } \color{#FF6800}{ - } \left ( \color{#FF6800}{ 2 } \left ( \color{#FF6800}{ 3 } \color{#FF6800}{ y } \right ) \color{#FF6800}{ \times } \color{#FF6800}{ 1 } \right ) + 1 ^ { 2 } \right )$
$\dfrac { 1 } { 9 } \left ( \left ( \color{#FF6800}{ 3 } \color{#FF6800}{ y } \right ) ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \left ( \color{#FF6800}{ 2 } \left ( \color{#FF6800}{ 3 } \color{#FF6800}{ y } \right ) \color{#FF6800}{ \times } \color{#FF6800}{ 1 } \right ) \color{#FF6800}{ + } \color{#FF6800}{ 1 } ^ { \color{#FF6800}{ 2 } } \right )$
 Organize the expression using $A^{2} ± 2AB + B^2 = (A ± B)^{2}$
$\dfrac { 1 } { 9 } \left ( \color{#FF6800}{ 3 } \color{#FF6800}{ y } \color{#FF6800}{ - } \color{#FF6800}{ 1 } \right ) ^ { \color{#FF6800}{ 2 } }$
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