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Calculate the value
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Factorize by the perfect square formula
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$9x ^{ 2 } -3x+ \dfrac{ 1 }{ 4 }$
$\dfrac { 36 x ^ { 2 } - 12 x + 1 } { 4 }$
Arrange the rational expression
$\color{#FF6800}{ 9 } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ 3 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ \dfrac { 1 } { 4 } }$
$ $ Calculate the expression as a fraction format $ $
$\color{#FF6800}{ \dfrac { 36 x ^ { 2 } - 12 x + 1 } { 4 } }$
$\dfrac { 1 } { 4 } \left ( 6 x - 1 \right ) ^ { 2 }$
Express as the perfect square formula
$\color{#FF6800}{ 9 } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ 3 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ \dfrac { 1 } { 4 } }$
$ $ Bind the expressions with the common factor $ \dfrac { 1 } { 4 }$
$\color{#FF6800}{ \dfrac { 1 } { 4 } } \left ( \color{#FF6800}{ 36 } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ 12 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \right )$
$\dfrac { 1 } { 4 } \left ( \color{#FF6800}{ 36 } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } - 12 x + 1 \right )$
$ $ Present as the shape of the power $ $
$\dfrac { 1 } { 4 } \left ( \color{#FF6800}{ 6 } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } - 12 x + 1 \right )$
$\dfrac { 1 } { 4 } \left ( \color{#FF6800}{ 6 } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } - 12 x + 1 \right )$
$ $ Binding the power $ $
$\dfrac { 1 } { 4 } \left ( \left ( \color{#FF6800}{ 6 } \color{#FF6800}{ x } \right ) ^ { \color{#FF6800}{ 2 } } - 12 x + 1 \right )$
$\dfrac { 1 } { 4 } \left ( \left ( 6 x \right ) ^ { 2 } - 12 x + \color{#FF6800}{ 1 } \right )$
$ $ Present as the shape of the power $ $
$\dfrac { 1 } { 4 } \left ( \left ( 6 x \right ) ^ { 2 } - 12 x + \color{#FF6800}{ 1 } ^ { \color{#FF6800}{ 2 } } \right )$
$\dfrac { 1 } { 4 } \left ( \left ( 6 x \right ) ^ { 2 } \color{#FF6800}{ - } \color{#FF6800}{ 12 } \color{#FF6800}{ x } + 1 ^ { 2 } \right )$
$ $ Change the term in the middle $ $
$\dfrac { 1 } { 4 } \left ( \left ( 6 x \right ) ^ { 2 } \color{#FF6800}{ - } \left ( \color{#FF6800}{ 2 } \left ( \color{#FF6800}{ 6 } \color{#FF6800}{ x } \right ) \color{#FF6800}{ \times } \color{#FF6800}{ 1 } \right ) + 1 ^ { 2 } \right )$
$\dfrac { 1 } { 4 } \left ( \left ( \color{#FF6800}{ 6 } \color{#FF6800}{ x } \right ) ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \left ( \color{#FF6800}{ 2 } \left ( \color{#FF6800}{ 6 } \color{#FF6800}{ x } \right ) \color{#FF6800}{ \times } \color{#FF6800}{ 1 } \right ) \color{#FF6800}{ + } \color{#FF6800}{ 1 } ^ { \color{#FF6800}{ 2 } } \right )$
$ $ Organize the expression using $ A^{2} ± 2AB + B^2 = (A ± B)^{2}$
$\dfrac { 1 } { 4 } \left ( \color{#FF6800}{ 6 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 1 } \right ) ^ { \color{#FF6800}{ 2 } }$
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