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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 $x$?
 

Thanks for the help

 Jan 27, 2020
 #1
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Factor  (x2 + y2 - z2)2 - 4x2y2

--->      (x2 + y2 - z2)2 - (2xy)2

Factor as the difference of two squares:

--->     [ ( x2 + y2 - z2 ) + (2xy) ] · [ ( x2 + y2 - z2 ) - (2xy) ] 

Rewrite:

--->     [ x2 + 2xy + y2 - z2 ] · [  x2 - 2xy + y2 - z2 ] 

Factor:

--->     [ (x + y)2 - z2 ] · [  (x - y)2 - z2 ] 

Factor as the difference of two squares:

--->     [ (x + y + z)(x + y - z) ] · [ (x - y + z)(z - y - z) ]

 

Answer:   (x + y + z)(x + y - z)(x - y + z)(z - y - z) 

 Jan 27, 2020

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