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Factorize the expression
Answer
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$16x ^{ 4 } -625y ^{ 4 }$
$\left ( 2 x - 5 y \right ) \left ( 2 x + 5 y \right ) \left ( 4 x ^ { 2 } + 25 y ^ { 2 } \right )$
Arrange the expression in the form of factorization..
$\color{#FF6800}{ 16 } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 4 } } \color{#FF6800}{ - } \color{#FF6800}{ 625 } \color{#FF6800}{ y } ^ { \color{#FF6800}{ 4 } }$
$ $ Factorize to use the polynomial formula of sum and difference $ $
$\left ( \color{#FF6800}{ 4 } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ 25 } \color{#FF6800}{ y } ^ { \color{#FF6800}{ 2 } } \right ) \left ( \color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 5 } \color{#FF6800}{ y } \right ) \left ( \color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 5 } \color{#FF6800}{ y } \right )$
$\left ( \color{#FF6800}{ 4 } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ 25 } \color{#FF6800}{ y } ^ { \color{#FF6800}{ 2 } } \right ) \left ( \color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 5 } \color{#FF6800}{ y } \right ) \left ( \color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 5 } \color{#FF6800}{ y } \right )$
$ $ Sort the factors $ $
$\left ( \color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 5 } \color{#FF6800}{ y } \right ) \left ( \color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 5 } \color{#FF6800}{ y } \right ) \left ( \color{#FF6800}{ 4 } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ 25 } \color{#FF6800}{ y } ^ { \color{#FF6800}{ 2 } } \right )$
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