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Factorize by the sum and difference formula
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Factorize the expression
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$\left ( 3 x - y + z \right ) \left ( 3 x - y - z \right )$
Factorization using perfect square expression, and sum and difference formula
$\color{#FF6800}{ 9 } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ 6 } \color{#FF6800}{ x } \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ y } ^ { \color{#FF6800}{ 2 } } - z ^ { 2 }$
$ $ Express as the perfect square formula $ $
$\left ( \color{#FF6800}{ 3 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ y } \right ) ^ { \color{#FF6800}{ 2 } } - z ^ { 2 }$
$\left ( \color{#FF6800}{ 3 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ y } \right ) ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ z } ^ { \color{#FF6800}{ 2 } }$
$ $ Factorize to use the polynomial formula of sum and difference $ $
$\left ( \color{#FF6800}{ 3 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ z } \right ) \left ( \color{#FF6800}{ 3 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ y } \color{#FF6800}{ - } \color{#FF6800}{ z } \right )$
$\left ( 3 x - y + z \right ) \left ( 3 x - y - z \right )$
Factorization using perfect square expression, and sum and difference formula
$\color{#FF6800}{ 9 } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ 6 } \color{#FF6800}{ x } \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ y } ^ { \color{#FF6800}{ 2 } } - z ^ { 2 }$
$ $ Express as the perfect square formula $ $
$\left ( \color{#FF6800}{ 3 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ y } \right ) ^ { \color{#FF6800}{ 2 } } - z ^ { 2 }$
$\left ( \color{#FF6800}{ 3 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ y } \right ) ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ z } ^ { \color{#FF6800}{ 2 } }$
$ $ Factorize to use the polynomial formula of sum and difference $ $
$\left ( \color{#FF6800}{ 3 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ z } \right ) \left ( \color{#FF6800}{ 3 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ y } \color{#FF6800}{ - } \color{#FF6800}{ z } \right )$
$\left ( 3 x - y - z \right ) \left ( 3 x - y + z \right )$
Arrange the expression in the form of factorization..
$\color{#FF6800}{ 9 } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ 6 } \color{#FF6800}{ x } \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ y } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ z } ^ { \color{#FF6800}{ 2 } }$
$ $ Factorize to use perfect square expression, and the sum and difference formula $ $
$\left ( \color{#FF6800}{ 3 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ z } \right ) \left ( \color{#FF6800}{ 3 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ y } \color{#FF6800}{ - } \color{#FF6800}{ z } \right )$
$\left ( \color{#FF6800}{ 3 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ z } \right ) \left ( \color{#FF6800}{ 3 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ y } \color{#FF6800}{ - } \color{#FF6800}{ z } \right )$
$ $ Sort the factors $ $
$\left ( \color{#FF6800}{ 3 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ y } \color{#FF6800}{ - } \color{#FF6800}{ z } \right ) \left ( \color{#FF6800}{ 3 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ z } \right )$
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