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Factor x^2+y^2-z^2)^2-4x^2y^2 as the product of four polynomials of degree 1 , each of which has a positive coefficient of x.

waffles  Jan 18, 2018
 #1
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( x^2+y^2-z^2)^2 - 4x^2y^2

 

 ( [ (x^2 + y^2  - z^2 ]  +  2xy )   ( [ x^2 + y^2 -z^2] - 2xy )

 

(  [ x^2 + 2xy + y^2 ]  - z^2  )  (  [ x^2 - 2xy + y^2]  - z^2 )

 

(  ( x + y)^2  - z^2 )   (  ( x - y)^2  - z^2 )

 

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

 

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

 

 

cool cool cool

CPhill  Jan 18, 2018

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