Question

solve plz
$( x {}^{2} + y {2} - z {2})^{2} - 4x ^{2}y {2}$
factorizeeee

Answer 1

solution :

( x² + y² - z² )² - 4x²y²

= ( x² + y² - z² )² - ( 2xy )²

= ( x² + y² - z² + 2xy )( x² + y² - z² - 2xy )

[ ∵ a² - b² = ( a + b )( a - b ) ]

= [ ( x² + y² + 2xy ) - z² ] [ ( x² + y² -2xy ) - z² ]

= [ ( x + y )² - z² ] [ ( x - y )² - z² ]

= ( x + y +z )( x + y - z )( x - y + z )( x -y - z)

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