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Factorize the expression
Answer
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$25x ^{ 2 } -9y ^{ 2 } +12yz-4z ^{ 2 }$
$\left ( 5 x - 3 y + 2 z \right ) \left ( 5 x + 3 y - 2 z \right )$
Arrange the expression in the form of factorization..
$\color{#FF6800}{ 25 } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ 9 } \color{#FF6800}{ y } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ 12 } \color{#FF6800}{ y } \color{#FF6800}{ z } \color{#FF6800}{ - } \color{#FF6800}{ 4 } \color{#FF6800}{ z } ^ { \color{#FF6800}{ 2 } }$
$ $ Factorize to use perfect square expression, and the sum and difference formula $ $
$\left ( \color{#FF6800}{ 5 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 3 } \color{#FF6800}{ y } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ z } \right ) \left ( \color{#FF6800}{ 5 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 3 } \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ 2 } \color{#FF6800}{ z } \right )$
$\left ( \color{#FF6800}{ 5 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 3 } \color{#FF6800}{ y } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ z } \right ) \left ( \color{#FF6800}{ 5 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 3 } \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ 2 } \color{#FF6800}{ z } \right )$
$ $ Sort the factors $ $
$\left ( \color{#FF6800}{ 5 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 3 } \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ 2 } \color{#FF6800}{ z } \right ) \left ( \color{#FF6800}{ 5 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 3 } \color{#FF6800}{ y } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ z } \right )$
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